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Question

The equation of the plane through the points (0, -4, -6) and (-2, 9, 3) and perpendicular to the plane x – 4y – 2z = 8 is


A
3x + 3y – 2z = 0
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B
x – 2y + z = 2
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C
2x + y – z = 2
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D
5x + 3y + 2z = 0
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Solution

The correct option is C 2x + y – z = 2
Equation of plane through (0, -4, -6) is
a(x- 0)+b (y+4)+c (z+6)=0                                                                                                      ………(i)
Point (-2, 9, 3) lies on Eq. (i), then
-2a + 13b + 9c = 0                                                                                              ………(ii)
also required plane is perpendicular to x – 4y – 2z = 8
a – 4b – 2c = 0                                                                                                    ………(iii)
From Eqs. (i), (ii), (iii) we get
∣ ∣xy+4z+62139142∣ ∣=0
ie,         2x + y – z – 2 = 0

Mathematics

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