Determine the vector $\vec d$ perpendicular to the z axis and to the vector $\vec a$ = 8$\vec i$ − 15$\vec j$ + 3$\vec k$ , so that its intensity is 50 and forms an acute angle with the x axis.
So here is what I know:
$\vec{d} = (d_1, d_2, d_3) $
$ \vec{a} \cdot \vec{d} = 0 $
This translates into $ 8d_1 - 15d_2 + 3d_3 = 0 $
$ | \vec{d} | = 50 $ ->
$ \sqrt{d_1^2 + d_2^2 + d_3^2}=50 $
But I dont know what does it mean that vector $\vec d$ is perpendiuclar to the z axis, and that vector $\vec d$ forms an acute angle with x axis. I would be thankful for any help.