Question

Find the angle,theta between vectors; round to two decimal places:
A) u=<3,2>, v=<4,0>
B) u= 2i-3j, v=i-2j

Answer 1

familiar wid "dot product" ?

Answer 2

kind of

Answer 3

\(\large \vec{a} \bullet \vec{b} = |\vec{a} | ~|\vec{b}|~ \cos(\color{red}{\theta})\)

Answer 4

there is the angle.. take dot product and solve it

Answer 5

A) u=<3,2>, v=<4,0>

first find below :

\(u.v = ?\)
\(|u| = ?\)
\(|v| = ?\)

Answer 6

3,2?
4,0?

Answer 7

yes, \(u . v = <3, 2> . <4, 0> = 3*4 + 2*0 = 12\)

Answer 8

\(|u| = \sqrt{3^2 + 2^2} = \sqrt{13}\)

\(|v| = \sqrt{4^2 + 0^2} = 4\)

Answer 9

plug these 3 values in the dot product formula

Answer 10

\(\large \vec{a} \bullet \vec{b} = |\vec{a} | ~|\vec{b}|~ \cos(\color{red}{\theta})\)

\(\large 12 = \sqrt{13} \times 4~ \cos(\color{red}{\theta})\)

Answer 11

see if u can solve \(\color{red}{\theta}\)

Answer 12

I cant

Answer 13

okay, its easy.. u need to use calucaltor :

\(\large 12 = \sqrt{13} \times 4~ \cos(\color{red}{\theta})\)

\(\large \frac{3}{\sqrt{13}} = \cos (\color{red}{\theta})\)

Answer 14

fine so far ?

Answer 15

yea, im following you

Answer 16

\(\large \frac{3}{\sqrt{13}} = \cos (\color{red}{\theta})\)


take \(\cos^{-1}\) both sides

\(\large \cos^{-1}( \frac{3}{\sqrt{13}}) = \color{red}{\theta} \)

Answer 17

use ur calculator

Answer 18

http://www.wolframalpha.com/input/?i=arccos%283%2Fsqrt%2813%29%29

Answer 19

rounding to two decimal places 0.59?

Answer 20

give them angle in DEGREES..

Answer 21

0.59 is the angle in radians...
but usually ur teachers expect u to give angle in DEGREEs..

Answer 22

okay, so 33.69 degrees

Answer 23

Correct !!

Answer 24

awesome!

Answer 25

and I do b the same way

Answer 26

yes, same way :

find below 3 things :
1) u.v
2) |u|
3) |v|

Answer 27

and plug them in "dot product" formula

Answer 28

u wana give it a try ? :)

Answer 29

B) u= 2i-3j, v=i-2j

Answer 30

yea, give me a few minutes

Answer 31

take ur time

Answer 32

okay so I have 8=√13*√5 cos Θ

Answer 33

im a little lost on what's next

Answer 34

Excellent !

Answer 35

8=√13*√5 cos Θ

Answer 36

isolate cos Θ first

Answer 37

so I would divide by √5?

Answer 38

divide by √13*√5

Answer 39

so i would put in my calculator √13/√5?

Answer 40

nope

Answer 41

8=√13*√5 cos Θ

divide √13*√5 both sides

8/(√13*√5 ) = cos Θ

Answer 42

take \(\cos^{−1}\) both sides to get Θ

Answer 43

http://www.wolframalpha.com/input/?i=arccos%288%2F%28sqrt%2813%29*sqrt%285%29%29%29

Answer 44

oh okay. I think im getting the hang of it. You are very helpful. Thank you again.

Answer 45

np :) rounded to two decimal places teh angle wud be \(7.13\) degrees