If A and B are the feet of the perpendiculars drawn from (1, 2, 3) to planes YZ and ZX , then the equation of the plane passing through the points A, B and the origin is

Step-by-step solution

Let the given point be P(1, 2, 3) . The foot of the perpendicular from P to the YZ -plane ( x = 0 ) is A(0, 2, 3) . The foot of the perpendicular from P to the ZX -plane ( y = 0 ) is B(1, 0, 3) . The equation of the plane passing through the origin (0, 0, 0) is ax + by + cz = 0 . Since the plane passes through A(0, 2, 3) and B(1, 0, 3) , we have: 2b + 3c = 0 a + 3c = 0 Solving these equations, we get a = -3c and b = - 3 2 c . Substituting the values of a and b in the equation of the plane: -3cx - 3 2 cy + cz = 0 Di