Question

Find the angle between the given vectors to the nearest degree.

a. 110.7

b.71.6

c. 108.4

d. 112.3

Answer 1

I believe the answer is c

Answer 2

c. 108.4

Explanation:

cos theta = (u dot v)/ (||u|| ||v||)

where dot stands for dot product and || || is the magnitude

u = (1,5) v= (7,-4)

u dot v = (1*7 + 5*-4) = 7-20 = -13

||u|| = sqrt( 1^2 +5^2) = sqrt(1+25) = sqrt(26)

||v|| = sqrt(7^2 + (-4)^2) = sqrt(49+16) = sqrt(65)

cos theta = -13/ sqrt(26) sqrt(65)

cos theta = -13 /sqrt(1690)

theta = arccos (-13/sqrt(1690))

theta = 108.43