Given v2ij and w3i8j find the angle between v and w What is

Given v=2ij and w=3i+8j, find the angle between v and w.

What is the angle between v and w?

Solution

v=2ij and w=3i+8j

|v|=[2²+(1)²] and |w|=[3²+8²]

|v|=5 and |w|=73

v.w =(2ij).(3i+8j)

v.w =(2*3)-(-1*8)

v.w =6+8

v.w =14

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

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

cos(v,w) =14/(5*73)

cos(v,w) =0.819288

(v,w) =34.9864^o

(v,w) =35^o

angle between v and w is approximately 35^o