8x – 13y + 15z + 13 = 0

Sol. ∴ Equation of plane through (3, 4, 1) is

a(x – x 1 ) + b(y – y 1 ) + c(z – z 1 ) = 0 ⇒ a(x – 3) + b(y – 4)+ c(z – 1) = 0 ...(i)

∴ –3a – 3b – c = 0 ⇒ 3a + 3b + c = 0 ...(ii)

Also the plane (i) is parallel to the line

∴ a 1 a 2 + b 1 b 2 + c 1 c 2 = 0 ⇒ 2a + 7b + 5c = 0 ...(iii)

Eliminating a, b, c from (i), (ii) and (iii), we get

= 0 ⇒ (x – 3) (15 – 7) – (y – 4) (15 – 2) + (z – 1) (21 – 6) = 0

8(x – 3) – 13(y – 4) + 15(z – 1) = 0 ⇒ 8x – 24 – 13y + 52 + 15z – 15 = 0

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