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Question

Equation of the plane perpendicular to the plane x – 2y + 5z + 1 = 0 which passes through the points (2, –3, 1) and (–1, 1, –7) is given by :

A
4x – 4y + z + 7 = 0
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B
4x + 7y + 2z + 11 = 0
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C
2x + y – z = 0
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D
2x + y – 3z = 0
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Solution

The correct option is B 4x + 7y + 2z + 11 = 0
Equation of the plane through (2, –3, 1) is
a(x – 2) + b(y + 3) + c(z – 1) = 0
It passes through (–1, 1, –7) and perpendicular to the plane x – 2y + 5z + 1 = 0
–3a+ 4b – 8c = 0 and a – 2b + 5c = 0
a4=b7=c2
Hence, equation of required plane is
4x + 7y + 2z + 11 = 0

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