Practice!

Sample Problem

Use the Law of Cosines to find the angle θ between v=i-j, w=2i+j. Assume that 0°<θ<180°.

Θ=° Round your answer to three decimal places.

Solution

v=<1, -1>

w=<2, 1>

w-v=<2-1, 1-(-1)>=<1, 2>

||v||=√2

||w||=√5

||w-v||=√5

Cos θ={||v||2+||w||2-||w-v||2}/(2||v||*||w||)

=(√2)2+(√5)2-(√5)2/(2√2√5)=2/2√10=1/√10

Cos-1(1/√10)71.565°