Question

Look at attachment....

Answer 1

Would you use the equation:

\[(x _{1},y _{1}) + (x _{2}, y _{2}) = (x _{1}+x _{2}, y _{1} + y _{2})\]

Answer 2

@vinnv226 @ganeshie8

Answer 3

Or this one:

\[\sqrt{x ^{2}+y ^{2}}\]

Answer 4

i think u need to take dot product

Answer 5

a.b = |a||b|cos(theta)

Answer 6

Oh ok. So the answer would be 23?

Answer 7

i did vectors very long back
@terenzreignz

Answer 8

But it was good... @ganeshie8
Find their dot product, @agupta

Answer 9

the dot product of two vectors goes like this:
\[\Large \left<x_1 , y_1\right>\cdot \left<x_2, y_2\right>=x_1x_2 +y_1y_2\]
And as you can see, it's a scalar.

Answer 10

So the answer would be 23?
Because this guy in the video but the dot product over the magnitude...

http://www.youtube.com/watch?v=WDdR5s0C4cY

Answer 11

I don't know the answer (yet).
But what is their dot product?

Answer 12

\[(2,-5) \times (4,-3) = 8+15 = 23\]

Answer 13

Okay. And their magnitudes?
What are their respective magnitudes?

Answer 14

\[\left| v _{1} \right| = \sqrt{2^{2}+(-5)^{2}} = \sqrt{4+25} = \sqrt{29}\]

Answer 15

Yes... and the other one?

Answer 16

\[\left| v _{2} \right| = \sqrt{4^{2} + (-3)^{2}} = \sqrt{16+9} = \sqrt{25} = 5\]

Answer 17

okay. So you now use this fact :
\[\large \cos\theta = \frac{v_1\cdot v_2}{||v_1|| \ ||v_2||}\]

Answer 18

\(\large \frac{ 23 }{ \sqrt{29} \times5 } \)

Answer 19

\[\frac{ 23 }{ \sqrt{29} \times 5 } = 0.85?\]

Answer 20

and that's the cosine. Now take the inverse cosine of that

Answer 21

\[\cos^{-1} (0.854) = 1\]

Answer 22

No way... o.O

Answer 23

Is it wrong???? @terenzreignz

Answer 24

It's just hard to believe it resulted in an integer...

Answer 25

Run it through again

Answer 26

I still got the same answer

Answer 27

I wonder...

Answer 28

you need to put calculator in inverse mode
cos(0.854) = 1
cos^-1(0.854) \(\ne\) 1

Answer 29

Why did I not consider that :D

Answer 30

Sorry my phone calculator is messed up. I got with my other calculator

cos^-1 (0.854)= 0.5472

Answer 31

@terenzreignz @sara12345

Answer 32

change it to degrees mode

Answer 33

cos^-1 (0.854) = 31.35

Answer 34

1) Angle between two vectors a & b is given by cos(θ) = |a.b|/[|a|*|b|]

2) Here a = v1. |v1| = √29; |v2| = 5

(v1).(v2) = (2x4) + (-5x-3) = 8 + 15 = 23

So cos(θ) = 23/(5*√29)

Nearly θ = 31.35°

Answer 35

Is this answer always expressed in degrees or in radians?

Answer 36

there is a \( ^o\) in your question after the blank... so they want you express it in degrees