1.

Find the equation of the plane through (4,5, -6) and parallel to the plane 2x + 3y + 5z + 6 = 0

Answer» Let the required plane be P: Ax + By +Cz + D = 0

Given P//P1: 2x + 3y + 5z + 6 = 0, hence their normals will also be parallel, & will have the same direction ratios.

Hence, P: 2x + 3y + 5z + D = 0

Since the point (4, 5, -6) lies on P, it will satisfy it's equation.

Replacing the values:

2(4) + 3(5) +5(-6) + D = 0

D = 30 -15 - 8 = 7

Equation of P: 2x + 3y + 5z + 7 = 0

Hence found.


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