Question

Find the angle between the given vectors to the nearest tenth of a degree.

u = <-5, -4>, v = <-4, -3>
@agent0smith

Answer 1

a · b = |a| × |b| × cos(θ)

| | means magnitude.
a*b means dot product

Answer 2

http://www.mathsisfun.com/algebra/vectors-dot-product.html

Answer 3

i'm confused ...

Answer 4

Know how to find dot product? It's easy.

a = <s, t> and b = <x, y>

a·b = s*x + t*y

Answer 5

Determine whether the vectors u and v are parallel, orthogonal, or neither.

u = <6, -2>, v = <8, 24>

Answer 6

We haven't finished the first question... and that one uses the same method.

Answer 7

a = <s, t> and b = <x, y>

a·b = s*x + t*y


do that for

u = <-5, -4>, v = <-4, -3>

u·v = ?

Answer 8

i got 1.8

Answer 9

@agent0smith

Answer 10

How?

Multiply the x components together.
Multiply the y components together.

Add the two together

u = <-5, -4>, v = <-4, -3>

u·v = (-5)*(-4) + (-4)*(-3)

Answer 11

i got it as my final answer

Answer 12

for that 32

Answer 13

32 = |u| × |v| × cos(θ)

where
|u| = sqrt(5^2 + 4^2)
|v| = sqrt(4^2 + 3^2)

if you did something like this, and found theta you're right. I haven't checked the answer.

Answer 14

yeah i did that, do you think im right

Answer 15

Yes, 1.8 degrees is correct!

Answer 16

Yay c:

Answer 17

http://www.wolframalpha.com/input/?i=arccos%2832%2F%28sqrt%285%5E2+%2B+4%5E2%29*sqrt%284%5E2+%2B+3%5E2%29%29%29

there it is :)

Answer 18

u = <6, -2>, v = <8, 24>

for this find u·v = ?

Answer 19

48,-48

Answer 20

@agent0smith

Answer 21

Dot product isn't a vector. you add the numbers.

Answer 22

Determine whether the vectors u and v are parallel, orthogonal, or neither.

u = <6, -2>, v = <8, 24>

Answer 23

Find the indicated dot product.

r = <9, -7, -8>, v = <3, 4, 7>, w = <6, -9, 7>

v ⋅ w
@agent0smith

Answer 24

Same as above.

v = <3, 4, 7>, w = <6, -9, 7>

v ⋅ w =

multiply the x's, y's and z's

Answer 25

Same way you did it with the ones above, just this time you have two extra numbers to multiply.

Answer 26

18,-36,49?

Answer 27

Dot product isn't a vector, you add the numbers.

Answer 28

so 31

Answer 29

That's your answer :)

Answer 30

Express the complex number in trigonometric form.

-3 + 3 square root of threei

Answer 31

Um, you'll have to find the r, which is the magnitude... sqrt( 3^2 + (3sqrt3)^2 )

and then find the angle. Tan theta = -3/(3sqrt3)

Answer 32

i got something completly off

Answer 33

...?