Find the matrix of the linear transformation on R 2 given by orthogonal projection onto line L containing the origin, angle theta with x-axis

Question

I don't know where to even start on this one. Can someone help? I know that I need to find the projection matrix, but I cannot visualise this question.

Answer 1

HINT

Recall that the projection onto a vector is given by

$$p = ax = a\frac{a^Tb}{a^Ta}$$

and in matrix form

$$p = ax = a\frac{a^Tb}{a^Ta}=\frac{aa^T}{a^Ta}b=Pb$$

refer to Projections onto subspaces by MIT for more details.