Question

help please :)
Find | |U + V| | given the vectors U = <0, 4> and V = <3, -5>.
a)
b) 3
c) 10
d) 2

Answer 1

:)

Answer 2

U+V=<0,4>+<3,-5> = <0+3,4-5>=<3,-1>
None of the answers is suitable for ||U+V|| (magnitude) unless (c) reads sqrt(10).

Answer 3

crap sorry. wrong one

Answer 4

Find the angle between the vectors U = <-2, -1> and V = <-3, 1>.
a) 58°
b) 135°
c) 45°
d) 35°

Answer 5

Do you know dot products?

Answer 6

yes

Answer 7

Do you know how to get the cosine between two vectors, given the two vectors?

Answer 8

i do not think so

Answer 9

How about finding unit vector from a vector?

Answer 10

could you just give me the answer? haha. i konw the steps but i dont really know what they're called

Answer 11

We're not supposed to directly give the answers. There's Wolfram which will give you answers blindly. You come here because you'd like to know how to work out the problem, unless I am mistaken.

Answer 12

yeah, you're right. okay, just tell me how to set it up

Answer 13

Basically, you would find the unit vector corresponding to each vector, say u for U, and v for V. Then the dot product (u.v) is the cosine of the angle between them.
Try and see if you can work it out.

Answer 14

im struggling with this.

Answer 15

To find the unit vector, you would divide each element by the magnitude.
U=<-2,-1>, and ||U||=sqrt((-2)^2+(-1)^2)=sqrt(5)
So unit vector u=<-2/sqrt(5), -1/sqrt(5)>, or for simplicity,
u=(1/sqrt(5))<-2,-1>
Do the same for V.
Find the dot product u.v and simplify to get cosine(theta).

Answer 16

You can post a reply for each step if it is too long to do in one shot.

Answer 17

okay i got 45

Answer 18

hopefully thats right

Answer 19

a dot b = |a||b|cos(theta)
so cos^(-1)(a dot b)/(|a||b|) = theta

Answer 20

That's what I got too!

Answer 21

okay cool! thanks guys

Answer 22

You're welcome! :)