Question

Find the angle between the given vectors to the nearest tenth of a degree.

u = <8, 7>, v = <9, 7>

Answer 1

Angle θ between two vectors is given by,
`\theta =cos^(-1)( (u \cdot v)/(|u||v|) )`; where
`u \cdot v=8(9)+(7)(7)=72+49=121`;
`|u|= \sqrt{ 8^(2) + 7^(2) } = √(64+49) = √(113)` and
`|v|=\sqrt{ 9^(2) + 7^(2) } = √(81+49) = √(130)`.
Therefore,
`\theta =cos^(-1)( (121)/( √(113) * √(130) ) )=cos^(-1)0.9983=3.3^o`