Question

Find two unit vectors that make an angle of 60° with v = ‹6, 8›. Give your answers correct to three decimal places.

Answer 1

Reduce v to a unit vector, v1=<3/5,4/5>
Then pre-multiply by the rotation matrix
\[\left[\begin{matrix}\cos(\theta) & -\sin(\theta) \\ \sin(\theta) & \cos(\theta)\end{matrix}\right]\]
to get the rotated vectors using \( \theta = \pi/3 or -\pi/3 \).