Determining Orthogonal Plane from 2 other points

Question

I am preparing for an upcoming test and this is a question I have some confusion about.

Determine orthogonal plane, x - 2y - 3z = 5; -5x + 2y - 3z = 7;

Is the orthogonal plane simply just 6a - 4b = 0? Or have I misunderstood the question?

Answer 1

HINT

• consider the normal vectors of the two given planes $n_1=(1,-2,-3)$ and $n_2=(-5,2,-3)$
• use cross product to find $n_3=n_1\times n_2$