## anonymous 5 years ago Consider the following vectors. v = 9i + 2j, w = 4i + 3j (a) Find the dot product v·w. v·w = (b) Find the angle between v and w. Give your answer in degrees, and round it to 2 decimal places. Angle between v and w = State whether the vectors are parallel, orthogonal, or neither.

1. anonymous

dot product = (9 x 4 ) + (2 x 3 ) = 36 +6 =42

2. anonymous

length of u = |u| = sqrt ( 9^2 +2^2} = sqrt( 85) |w| = sqrt( 4^2 +3^3) = 5

3. anonymous

a . b = |a||b|cos(A) where A is the angle between them

4. anonymous

$A= \cos^{-1} \frac{a.b}{|a||b|}$

5. anonymous

the rest is calculator work

6. anonymous

lol is it orthogonal or parralel or neither?

7. anonymous

most likely neither , you have to calculate A

8. anonymous

I think its neither

9. anonymous

for orthonal A=90degrres, for parallel A=0 and otherwise its nither

10. anonymous

keyboard :|

11. anonymous

Sweet. It must be neither then.

12. amistre64

the slope of the vectors tell you if they are // or L or neither right? 3/4 and 2/9

13. amistre64

in R^3 space, the dot is easier to tell the relationship between vectors; but in the plane? y/x is the slope of a vector :)