Question

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.

Answer 1

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

Answer 2

length of u = |u| = sqrt ( 9^2 +2^2} = sqrt( 85)

|w| = sqrt( 4^2 +3^3) = 5

Answer 3

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

where A is the angle between them

Answer 4

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

Answer 5

the rest is calculator work

Answer 6

lol is it orthogonal or parralel or neither?

Answer 7

most likely neither , you have to calculate A

Answer 8

I think its neither

Answer 9

for orthonal A=90degrres, for parallel A=0

and otherwise its nither

Answer 10

keyboard :|

Answer 11

Sweet. It must be neither then.

Answer 12

the slope of the vectors tell you if they are // or L or neither right?

3/4 and 2/9

Answer 13

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 :)