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Question
If the line drawn from the point (–2, – 1, – 3) meets a plane at right angle at the point (1, – 3, 3), find the equation of the plane.
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Solution
Direction ratios of the normal to the plane are (1 + 2, – 3 + 1, 3 + 3)
⇒ (3, – 2, 6)
Equation of plane passing through one point (x1, y1, z1) is
a(x – x1) + b(y – y1) + c(z – z1) = 0
⇒ 3(x – 1) – 2(y + 3) + 6(z – 3) = 0
⇒ 3x – 3 – 2y – 6 + 6z – 18 = 0
⇒ 3x – 2y + 6z – 27 = 0
⇒ 3x – 2y + 6z = 27
Hence, the required equation is 3x – 2y + 6z = 27.
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