Given v 10i 3j and w 5i j find the angle between v and w

Given v = 10i - 3j and w = -5i - j, find the angle between v and w. What is the angle between v and w? degree

Solution

v=10i -3j ,w =-5i -j

|v|=[(10)²+(-3)²]=109

|w|=[(-5)²+(-1)²]=26

v.w =(10i -3j ).(-5i -j)

v.w =(10*-5) +(-3*-1)

v.w=-50 +3

v.w =-47

v.w =|v||w| cos

cos=-47/(10926)

=cos^-1(-47/(10926))

=152^o