Question

Find the equation of the plane passing through the point (1, -2, 1) and perpendicular to the line joining the points A(3, 2, 1) and B(1, 4, 2). 

Answer 1

Here, given that the plane passes through the point (1, -2, 1) and it is perpendicular to the line joining the points A(3, 2, 1) and B(1, 4, 2).
Direction ratios of its normal are < 1 – 3, 4 – 2, 2 – 1 > i.e., < -2, 2, 1 >
Hence, the required equation of the plane is
-2(x – 1) + 2(y + 2) + 1(z – 1) = 0
⇒ -2x + 2 + 2y + 4 + z – 1 = 0
⇒ -2x + 2y + z + 5 = 0
or 2x – 2y – z – 5 = 0