Long Answer TypeFind the image of the point (1, 3, 4) in the plane x – y + z = 5.
From P (1, 3, 4) , draw PM ⊥ plane and produce it to P'such that M is mid-point of PP’ Then P' (α,β, γ) is image of P.
Direction ratios of PM are 1, – 1, 1
The equations of PM are
Any point on it is M (r + 1, – r + 3, r + 4)
∵ M lies on plane (1)
∴ (r + 1)–(–r + 3)+.(r + 4) = 5, ∴ r + 1 + r – 3 + r + 4 = 5
∴ 3r = 3 ⇒ r = 1
∴ M is (2, 2, 5)
Since M is mid-point of PP'
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