Finding direction angles of a $3$D vector, with no points given

Question

How can I find directions angles of vector $\vec{A}$ which lies in coordinate plane $yz$ and makes angle $15^\circ$ with $(X,Y, \text{ and } Z)$ axis?

I want to know how to find the directions if they make $15^\circ$ with the $3$ axes.

Please explain in details.

Answer 1

Find a vector which lies in the $yz$-plane and makes an angle of $15^\circ$ with each of the $x$-, $y$-, and $z$-axes.

Any vector that lies in the $yz$-plane must be perpendicular, at a $90^\circ$ angle, to the $x$-axis.

Therefore, there is no vector that satisfies all of your conditions.