At what value of C does point A (1, -2, C) lie in the plane 3x-2y + z-10 = 0.

In order to find at what value of the parameter c the point with coordinates A (1; -2; c) lies in the plane 3x – 2y + z – 10 = 0, we will compose and solve the equation.

Let’s start by substituting the coordinates of point A into the equation of the plane, since it, based on the condition, belongs to a given plane and we get an equation with one variable.

So, let’s substitute x = 1; y = -2 and get:

3 * 1 – 2 * (-2) + z – 10 = 0;

3 + 4 + z – 10 = 0;

Transferring 3; 4 and -10 to the right side of the equation:

z = 10-3-4;

z = 10 – 7;

z = 3.

With c = 3.