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Co - ordinate Geometry 3D Geometry

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Equation of the plane passing through the point (1, 2, 3) and perpendicular to the plane x + 2y + 3z + 4 = 0 must pass through the point

A. (1, 0, 1)

B. (0, 0, 0)

C. (0, 0, –1)

D. (1, 0, –1)

E. None of the above

View Answer

Correct choice: C

Explanation:

Let equation of plane be
a(x–1) + b(y– 2) + c(z – 3) = 0 …………….(1)
Since it is perpendicular to the plane
x + 2y + 3z + 4 = 0
∴ a.1 + b.2 + c.3 = 0
a= –(2b + 3c)
From (1)
–(2b + 3c) (x–1) + b(y –2) + c(z –3) = 0
Or b{–2x + 2 + y –2} + c(–3x + 3 + z –3) = 0
(y – 2x) + c/b(z – 3x) = 0
Clearly it is always satisfied by (0, 0, 0)

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Eamcet Mathematics Co - ordinate Geometry 3D Geometry

Eamcet Mathematics
Co - ordinate Geometry 3D Geometry