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Three Dimensional Geometry
Question
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Find equation of a plane parallel to 2x – 3y + z + 9 = 0 and also passing through origin.  

Answer

Equation of any plane parallel to the plane
2x – 3y + z + 9 = 0 is
2x – 3y  + z +  k = 0    ..(1)
∴  it passes through origin (0, 0, 0)
∴  0 – 0 + 0 + k = 0 ⇒ k = 0
Putting k = 0 in (1), we get,
2x – 3y + z = 0
which is required equation of plane.

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Some More Questions From Three Dimensional Geometry Chapter

If α, β, γ are the angles which a line makes with the axes, prove that sin2α + sin2 β + sin2γ = 2.

Show that the points A(2, 3, – 4), B(1, –2, 3) and C (3, 8, –11) are collinear.