Question

find the angle between the given vectors to the nearest tenth of a degree. u = <2, -4>, v = <3, -8>

Answer 1

Angle θ between two vectors is given by,
`\theta =cos^(-1)( (u \cdot v)/(|u||v|) )`; where
`u \cdot v=2(3)+(-4)(-8)=6+32=38`;
`|u|= \sqrt{ 2^(2) + (-4)^(2) } = √(4+16) = √(20)` and
`|v|=\sqrt{ 3^(2) + (-8)^(2) } = √(9+64) = √(73)`.
Therefore,
`\theta =cos^(-1)( (38)/( √(20) * √(73) ) )=cos^(-1)0.9945=6.0^o`