Given v 3i j and w 9i 2j find the angle between v and w

Given v = 3i - j and w = 9i + 2j, find the angle between v and w. What is the angle between v and w? ____ degree (Type your answer in degrees. Do not round until the final answer Then round to the nearest tenth as needed)

Solution

given v=3i -j ,w=9i+2j

v.w=(3i -j).(9i+2j)=(3*9) +(-1*2) =27-2 =25

|v|=[3²+(-1)²] =10 ,|w|=[9²+2²]=85

cos(v,w) =v.w_/|v||w|

cos(v,w) =25_/1085

cos(v,w) =0.857493

(v.w)=30.964^o

abgle between v,w is 31.0^o