Question 1

The plane given by the equation 3x-4y+z-1=0 is perpendicular to the vector

<9,-12,3> and contains the point (0,0,1).

The answer is TRUE

Question 2

If A is a plane containing the point Psub1, Psub2, and Psub3 is any other point in 3-space, and Psub1Psub2 * Psub1Psub3 =0 , then Psub1Psub3 must be a normal vector for the plane.

The answer is FALSE

Question 3

The four points (-2,1,1), (0,2,3), (1,0,-1), and (5,4,7) all lies in the same plane.

The answer is TRUE

Could you please teach me how to solve them? Thank you very much.