Question

Find an equation of a plane making an angle of pi/2 with the plane -3x-y+4z=-2

Answer 1

you just need a vector that is perpendicular to the normal vector for your plane. Your normal is <3, 1, -4>. An orthogonal vector is
<4, 0, 3>

The plane through the origin with this as it's normal is
4x + 3z = 0