# u=−21iu=-21i Use the dot product to find the magnitude of u.

**TO KILL A MOCKINGBIRD**

**What do Scout’s thoughts about Boo Radley show us about her in Harper Lee’s To Kill a…**

In Chapter 31 of Harper Lee’s To Kill a Mockingbird, Scout’s thoughts about Arthur (Boo) Radley reveal a lot about just how much she had learned over the years and particularly at the exact moment…

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**SCIENCE**

**Does this make sense? Your tongue can stick to a flagpole because the freezing point of your…**

Interesting question! If you’ve ever had your fingers freeze to ice cubes you know that this can happen even without saliva involoved. It’s more likely that the freezing temperature of saliva is…

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**RAYMOND’S RUN**

**How does Squeaky’s attitude in “Raymond’s Run” by Toni Cade Bambara change by the end of the story?**

In the beginning of “Raymond’s Run” by Toni Cade Bambara, Squeaky is only concerned about herself and her handicapped brother, Raymond. She is very competitive and brags about being the best runner…

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**THE GIVER**

**Why can’t people have “stirrings” in Jonas’s society?**

There is no explicit reason given; however, we can deduce the answer to this based on other things we know about the society. We know that the stirrings are closely regulated by the community. In…

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**THE NIGHT THOREAU SPENT IN JAIL**

**In The Night Thoreau Spent in Jail, how does Henry’s non-conforming beliefs help convey the theme…**

Henry’s non- conforming beliefs in The Night Thoreau Spent in Jail enhance the play’s theme of freedom. Freedom is one of the most important themes in The Night Thoreau Spent in Jail. Henry’s non-…

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**SCIENCE**

**What is the white stuff called when you are melting styrofoam with nail polish remover and what…**

The white stuff that is left behind is still styrofoam, better known as polystyrene. Styrofoam is up to 95% trapped air, so when you put the styrofoam in an organic solvent, such as acetone, it…

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**SCIENCE**

**1 L of helium at 1 atm is compressed to 350 ml. What is the new pressure of gas?**

According to Boyle’s law, the pressure and volume of a gas are inversely proportional. The factor by which the pressure increased is the same as the factor by which the volume increased. Here’s the…

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**THE LADY OR THE TIGER?**

The princess is present at the arena when her lover has to undergo his trial. She is perhaps the only person present who knows which of the two doors conceals the tiger and which conceals the…

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**SCIENCE**

**An arrow is shot at 30o above the horizontal. Its velocity is 49 m/s, and it hits the target. a….**

Hello! I think we ignore air resistance. Then the only force acting on a flying arrow is the gravity force. It is acting downwards and gives an arrow constant acceleration of g (also downwards)….

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**SOCIAL SCIENCES**

**Explain how the four uses of output help us determine GDP.**

The four uses of output can also be defined as the four types of output. Together, they make up a country’s gross domestic product (GDP). Typically, most of a country’s output is used to…

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**ROMEO AND JULIET**

**What grim news is imparted at the beginning of Act 4 of Romeo and Juliet?**

The news is divulged to Friar Lawrence by the county Parris at the friar’s cell and concerns the fact that Juliet’s father has decided that she should marry him that Thursday. Parris tells the…

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**THE METAMORPHOSIS OF GREECE SINCE WORLD WAR II**

**What inference can you make about the reason Gregor is so worried?**

In the story “Metamorphosis,” Gregor is transformed into a bug. However, he soon becomes greatly worried (not about this physical change), but about going to work and providing for his family….

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**HISTORY**

**How did the Confederate government centralize its power during the Civil War?**

The Confederate States of America were established on a platform of a lack of centralized power. This new nation promoted the individual rights of states. In doing so, the Confederacy lacked the…

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**MATH**

**u=<−3,−2>,v=<−4,−1>u=<-3,-2>,v=<-4,-1> Find the projection of u onto v. Then write u as…**

You need to evaluate the projection of vector u onto vector v using the formula, such that: projv(u)=(u⋅v|v|2)⋅vprojv(u)=(u⋅v|v|2)⋅v You need to evaluate the product of vectors

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**MATH**

**u=<0,3>,v=<2,15>u=<0,3>,v=<2,15> Find the projection of u onto v. Then write u as the…**

You need to evaluate the projection of vector u onto vector v using the formula, such that: projv(u)=(u⋅v|v|2)⋅vprojv(u)=(u⋅v|v|2)⋅v You need to evaluate the product of vectors

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**MATH**

**u=<4,2>,v=<1,−2>u=<4,2>,v=<1,-2> Find the projection of u onto v. Then write u as the…**

You need to evaluate the projection of vector u onto vector v using the formula, such that: projv(u)=(u⋅v|v|2)⋅vprojv(u)=(u⋅v|v|2)⋅v You need to evaluate the product of vectors u=ux⋅i+uy⋅ju=ux⋅i+uy⋅j and

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**MATH**

**u=<2,2>,v=<6,1>u=<2,2>,v=<6,1> Find the projection of u onto v.**

The projection of vector u onto v can be evaluated using the following formula, such that: projv(u)=(u⋅v|v|)⋅vprojv(u)=(u⋅v|v|)⋅v First, evaluate the product of the vectors u⋅vu⋅v , such that:

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**MATH**

You need to use the formula of dot product to find the angle between two vectors, u=ux⋅i+uy⋅j,v=vx⋅i+vy⋅ju=ux⋅i+uy⋅j,v=vx⋅i+vy⋅j , such that: u⋅v=|u|⋅|v|⋅cos(θ)u⋅v=|u|⋅|v|⋅cos(θ) The angle between the vectors u and…

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**MATH**

You need to use the formula of dot product to find the angle between two vectors, u=ux⋅i+uy⋅j,v=vx⋅i+vy⋅j,u=ux⋅i+uy⋅j,v=vx⋅i+vy⋅j, such that: u⋅v=|u|⋅|v|⋅cos(θ)u⋅v=|u|⋅|v|⋅cos(θ) The angle between the vectors u and v…

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**MATH**

**u=2i−3j,v=4i+3ju=2i-3j,v=4i+3j Find the angle theta between the vectors.**

We want to get the angle, between vectors u = 2i -3j and v = 4i + 3j. By definition, the angle between two vectors is defined as follows (u and v are two vectors): .Hence, .

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**MATH**

**u=5i+5j,v=−6i+6ju=5i+5j,v=-6i+6j Find the angle theta between the vectors.**

We want to get the angle, θθ between vectors u = 5i + 5j and v = -6i + 6j. By definition, the angle between two vectors is defined as follows (u and v are two vectors):

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**MATH**

**u=−6i−3j,v=−8i+4ju=-6i-3j,v=-8i+4j Find the angle theta between the vectors.**

The angle between two vectors u and v is given by; cosθ=u.v|u||v|cosθ=u.v|u||v| u.v represent the vector dot product and |u| and |v| represents the magnitude of vectors. We know that in unit…

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**MATH**

**u=2i−j,v=6i+4ju=2i-j,v=6i+4j Find the angle theta between the vectors.**

The angle between two vectors u and v is given by; cosθ=u.v|u||v|cosθ=u.v|u||v| u.v represent the vector dot product and |u| and |v| represents the magnitude of vectors. We know that in unit…

1 educator answer

**MATH**

**u=2i−3j,v=i−2ju=2i-3j,v=i-2j Find the angle theta between the vectors.**

You need to use the formula of dot product to find the angle between two vectors, u=ux⋅i+uy⋅j,v=vx⋅i+vy⋅ju=ux⋅i+uy⋅j,v=vx⋅i+vy⋅j , such that: u⋅v=|u|⋅|v|⋅cos(θ)u⋅v=|u|⋅|v|⋅cos(θ) The angle between the vectors u and…

2 educator answers

**MATH**

**u=3i+4j,v=−2ju=3i+4j,v=-2j Find the angle theta between the vectors.**

You need to use the formula of dot product to find the angle between two vectors, u=ux⋅i+uy⋅j,v=vx⋅i+vy⋅ju=ux⋅i+uy⋅j,v=vx⋅i+vy⋅j , such that: u⋅v=|u|⋅|v|⋅cos(θ)u⋅v=|u|⋅|v|⋅cos(θ) The angle between the vectors u and…

1 educator answer

**MATH**

**u=<3,2>,v=<4,0>u=<3,2>,v=<4,0> Find the angle theta between the vectors.**

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**MATH**

**u=<1,0>,v=<0,−2>u=<1,0>,v=<0,-2> Find the angle theta between the vectors.**

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**MATH**

**u=−21iu=-21i Use the dot product to find the magnitude of u.**

The magnitude of a vector uu is the square root of its dot product by itself, because u⋅u=||u||⋅||u||⋅cos(θ),u⋅u=||u||⋅||u||⋅cos(θ), and θ=0,θ=0, cos(θ)=1.cos(θ)=1.I suppose that the magnitude of ii is 1. Then…

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**MATH**

**u=6ju=6j Use the dot product to find the magnitude of u.**

The magnitude of a vector uu is the square root of its dot product by itself, because u⋅u=||u||⋅||u||⋅cos(θ),u⋅u=||u||⋅||u||⋅cos(θ), and θ=0,θ=0, cos(θ)=1.cos(θ)=1.I suppose that the magnitude of ii is 1. Then…

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**MATH**

**u=12i−16ju=12i-16j Use the dot product to find the magnitude of u.**

The magnitude of a vector uu is the square root of its dot product by itself, because u⋅u=||u||⋅||u||⋅cos(θ),u⋅u=||u||⋅||u||⋅cos(θ), and θ=0,θ=0, cos(θ)=1.cos(θ)=1.I suppose that ii and jj are orthonormal….

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**MATH**

**u=20i+25ju=20i+25j Use the dot product to find the magnitude of u.**

The magnitude of a vector uu is the square root of its dot product by itself, because u⋅u=||u||⋅||u||⋅cos(θ),u⋅u=||u||⋅||u||⋅cos(θ), and θ=0,θ=0, cos(θ)=1.cos(θ)=1.I suppose that ii and jj are orthonormal….

1 educator answer

**MATH**

**u=<4,−6>u=<4,-6> Use the dot product to find the magnitude of u.**

The magnitude of a vector uu is the square root of its product by itself, because u⋅u=||u||⋅||u||⋅cos(θ),u⋅u=||u||⋅||u||⋅cos(θ), andθ=0,andθ=0, cos(θ)=1.cos(θ)=1. So ||u||=u⋅u−−−−√=<4,−6>⋅<4,−6>−−−−−−−−−−−−−−−−−−−−−−√=||u||=u⋅u=<4,-6>⋅<4,-6>=…

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**MATH**

**u=<−8,15>u=<-8,15> Use the dot product to find the magnitude of u.**

The magnitude of a vector uu is the square root of its product by itself, because u⋅u=||u||⋅||u||⋅cos(θ),u⋅u=||u||⋅||u||⋅cos(θ), and θ=0,θ=0, cos(θ)=1.cos(θ)=1. So ||u||=u⋅u−−−−√=<−8,15>⋅<−8,15>−−−−−−−−−−−−−−−−−−−−−−−−√=||u||=u⋅u=<-8,15>⋅<-8,15>=…

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**MATH**

**(v⋅u)−(w⋅v)(v⋅u)-(w⋅v) Use the vectors u=<3,3>u=<3,3>, and v=<−4,2>v=<-4,2>, and w=<3,−1>w=<3,-1>…**

The expression is a difference of two dot products, it is a scalar. For two vectors <x1,y1><x1,y1> and <x2,y2><x2,y2> their dot product is x1⋅x2+y1⋅y2.x1⋅x2+y1⋅y2. In this case

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**MATH**

**(u⋅v)−(u⋅w)(u⋅v)-(u⋅w) Use the vectors u=<3,3>u=<3,3>, and v=<−4,2>v=<-4,2>, and w=<3,−1>w=<3,-1>…**

The expression is a difference between two dot products, which are scalars. So the result is a scalar also. u⋅v=<3,3>⋅<−4,2>=3⋅(−4)+3⋅2=−6,u⋅v=<3,3>⋅<-4,2>=3⋅(-4)+3⋅2=-6, u⋅w=<3,3>⋅<3,−1>=3⋅3+3⋅(−1)=6,u⋅w=<3,3>⋅<3,-1>=3⋅3+3⋅(-1)=6, the…

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**MATH**

**2−||u||2-||u|| Use the vectors u=<3,3>u=<3,3>, and v=<−4,2>v=<-4,2>, and w=<3,−1>w=<3,-1> …**

22 is a scalar and ||u||||u|| is a scalar also (the magnitude of a vector). So the result is a scalar. The magnitude of a vector uu is u⋅u−−−−√.u⋅u. For u=<3,3>u=<3,3> ||u||=32+32−−−−−−√=32–√.||u||=32+32=32….

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**MATH**

**||w||−1||w||-1 Use the vectors u=<3,3>u=<3,3>, and v=<−4,2>v=<-4,2>, and w=<3,−1>w=<3,-1> to…**

||w||||w|| is a scalar (the magnitude of a vector) and 11 is a scalar also. So the result is a scalar. The magnitude of a vector ww is w⋅w−−−−√.w⋅w. For w=<3,−1>w=<3,-1>…

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**MATH**

**(u⋅2v)w(u⋅2v)w Use the vectors u=<3,3>u=<3,3>, and v=<−4,2>v=<-4,2>, and w=<3,−1>w=<3,-1> to…**

The dot product u⋅(2v)u⋅(2v) is a scalar, and its product with a vector ww is a vector. u⋅(2v)=<3,3>⋅(2⋅<−4,2>)=<3,3>⋅<−8,4>=3⋅(−8)+3⋅4=−12.u⋅(2v)=<3,3>⋅(2⋅<-4,2>)=<3,3>⋅<-8,4>=3⋅(-8)+3⋅4=-12.(−12)⋅<3,−1>=<−36,12>.(-12)⋅<3,-1>=<-36,12>. This is the…

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**MATH**

**(3w⋅v)u(3w⋅v)u Use the vectors u=<3,3>u=<3,3>, and v=<−4,2>v=<-4,2>, and w=<3,−1>w=<3,-1> to…**

3w⋅v3w⋅v is the dot product of two vectors, i.e. a scalar. (3w⋅v)⋅u(3w⋅v)⋅u is the product of this scalar and a vector, so it is a vector.

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**MATH**

**(v⋅u)w(v⋅u)w Use the vectors u=<3,3>u=<3,3>, and v=<−4,2>v=<-4,2>, and w=<3,−1>w=<3,-1> to find…**

v⋅uv⋅u is a dot product which is a scalar. (v⋅u)⋅w(v⋅u)⋅w is a scalar multiplied by a vector, i.e. a vector. v⋅u=u⋅v=<3,3>⋅<−4,2>=3⋅(−4)+3⋅2=−6.v⋅u=u⋅v=<3,3>⋅<-4,2>=3⋅(-4)+3⋅2=-6.So

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**MATH**

**(u⋅v)v(u⋅v)v Use the vectors u=<3,3>u=<3,3>, and v=<−4,2>v=<-4,2>, and w=<3,−1>w=<3,-1> to find…**

u⋅vu⋅v is a dot product which is a scalar. (u⋅v)⋅v(u⋅v)⋅v is a scalar multiplied by a vector, i.e. a vector. u⋅v=<3,3>⋅<−4,2>=3⋅(−4)+3⋅2=−6.u⋅v=<3,3>⋅<-4,2>=3⋅(-4)+3⋅2=-6. So

1 educator answer

**MATH**

**3u⋅v3u⋅v Use the vectors u=<3,3>u=<3,3>, and v=<−4,2>v=<-4,2>, and w=<3,−1>w=<3,-1> to find…**

(3u)⋅v,(3u)⋅v, which is the same as 3⋅(u⋅v),3⋅(u⋅v), is a dot product of two vectors. It is a scalar. For vectors <x1,y1><x1,y1> and <x2,y2><x2,y2> its dot product is x1⋅x2+y1⋅y2.x1⋅x2+y1⋅y2. In our case it is…

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**MATH**

**u⋅uu⋅u Use the vectors u=<3,3>u=<3,3>, and v=<−4,2>v=<-4,2>, and w=<3,−1>w=<3,-1> to find…**

u⋅uu⋅u is the dot product of two vectors. It is a scalar. For a vector <x,y><x,y> the dot product <x,y>⋅<x,y>=x2+y2.<x,y>⋅<x,y>=x2+y2. In our case u⋅u=32+32=9+9=18.u⋅u=32+32=9+9=18. This is the answer.

1 educator answer

**MATH**

**u=i−2j,v=−2i+ju=i-2j,v=-2i+j Find u⋅vu⋅v.**

You need to evaluate the product of the vectors u=ux⋅i+uy⋅j,v=vx⋅i+vy⋅ju=ux⋅i+uy⋅j,v=vx⋅i+vy⋅j , such that: u⋅v=ux⋅vx+uy⋅vyu⋅v=ux⋅vx+uy⋅vy u⋅v=(1)⋅(−2)+(−2)⋅(1)u⋅v=(1)⋅(-2)+(-2)⋅(1) u⋅v=−2−2u⋅v=-2-2 u⋅v=−4u⋅v=-4 Hence, evaluating…

1 educator answer

**MATH**

**u=3i+2j,v=−2i−3ju=3i+2j,v=-2i-3j Find u⋅vu⋅v.**

You need to evaluate the product of the vectors u=ux⋅i+uy⋅j,v=vx⋅i+vy⋅ju=ux⋅i+uy⋅j,v=vx⋅i+vy⋅j , such that: u⋅v=ux⋅vx+uy⋅vyu⋅v=ux⋅vx+uy⋅vy u⋅v=(3)⋅(−2)+2⋅(−3)u⋅v=(3)⋅(-2)+2⋅(-3) u⋅v=−6−6u⋅v=-6-6 u⋅v=−12u⋅v=-12 Hence, evaluating…

1 educator answer

**MATH**

**u=3i+4j,v=7i−2ju=3i+4j,v=7i-2j Find u⋅vu⋅v.**

You need to evaluate the product of the vectors u=ux⋅i+uy⋅j,v=vx⋅i+vy⋅ju=ux⋅i+uy⋅j,v=vx⋅i+vy⋅j , such that: u⋅v=ux⋅vx+uy⋅vyu⋅v=ux⋅vx+uy⋅vy u⋅v=(3)⋅(7)+4⋅(−2)u⋅v=(3)⋅(7)+4⋅(-2) u⋅v=21−8u⋅v=21-8 u⋅v=13u⋅v=13 Hence, evaluating…

1 educator answer

**MATH**

**u=4i−j,v=i−ju=4i-j,v=i-j Find u⋅vu⋅v.**

You need to evaluate the product of the vectors u=ux⋅i+uy⋅j,v=vx⋅i+vy⋅j,u=ux⋅i+uy⋅j,v=vx⋅i+vy⋅j, such that: u⋅v=ux⋅vx+uy⋅vyu⋅v=ux⋅vx+uy⋅vy u⋅v=(4)⋅(1)+(−1)⋅(−1)u⋅v=(4)⋅(1)+(-1)⋅(-1) u⋅v=4+1u⋅v=4+1 u⋅v=5u⋅v=5 Hence, evaluating…

1 educator answer

**MATH**

**u=<−2,5>,v=<−1,−8>u=<-2,5>,v=<-1,-8> Find u⋅vu⋅v.**

You need to evaluate the product of the vectors u=ux⋅i+uy⋅j,v=vx⋅i+vy⋅ju=ux⋅i+uy⋅j,v=vx⋅i+vy⋅j , such that: u⋅v=ux⋅vx+uy⋅vyu⋅v=ux⋅vx+uy⋅vy u⋅v=(−2)⋅(−1)+5⋅(−8)u⋅v=(-2)⋅(-1)+5⋅(-8) u⋅v=2−40u⋅v=2-40 u⋅v=−38u⋅v=-38 Hence, evaluating…

1 educator answer

**MATH**

**u=<−4,1>,v=<2,−3>u=<-4,1>,v=<2,-3> Find u⋅vu⋅v.**

You need to evaluate the product of the vectors u=ux⋅i+uy⋅j,v=vx⋅i+vy⋅ju=ux⋅i+uy⋅j,v=vx⋅i+vy⋅j , such that: u⋅v=ux⋅vx+uy⋅vyu⋅v=ux⋅vx+uy⋅vy u⋅v=(−4)⋅2+1⋅(−3)u⋅v=(-4)⋅2+1⋅(-3) u⋅v=−11u⋅v=-11 Hence, evaluating the product of…

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**MATH**

**u=<6,10>,v=<−2,3>u=<6,10>,v=<-2,3> Find u⋅vu⋅v.**

The dot product of vectors <x1, y1> and <x2, y2> is equal to x1*x2 + y1*y2. Here it is 6*(-2) + 10*3 = -12 + 30 = 18. This is the answer.

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