Hi Arez

Question 1

You need to find the direction vector of the line that is perpendicular to z-axis.

Any random vectors will be perpendicular to z-axis if the z-component is zero. Because the line passes through (5, -3, 4), it will have direction vector

There is other method but I think maybe this is the fastest one.

Question 2

Those two are Cartessian form of line equation. Have you learned how to change them to vector form of line equation?