(1)
2x + 3y – 2z = 5 and x + 2y – 3z = 8, we have
2A + 3B – 2C = 0 and A + 2B – 3C = 0
Solving these equations, we find A = – 5C and B = 4C Hence, the required
equation is
– 5C (x – 1) + 4 C (y + 1) + C(z – 2) = 0
i e 5x – 4y – z = 7
Example 28 Find the distance between the point P(6, 5, 9) and the plane determined
by the points A (3, – 1, 2), B (5, 2, 4) and C(– 1, – 1, 6)