Q32 of 34 Page 11

Find the coordinates of the point where the line through the points (3, -4, -5) and (2, -3, 1), crosses the plane determined by the points (1,2,3), (4,2, -3) and (0,4, 3).[CBSE 2017]

Equation of line through two given points is





Also equation of plane through three points is-




⇒ (x-1)(12) - (y-2)(-6) + (z-3)(6) = 0


⇒ 12x-12+6y-12+6z-18 = 0


⇒ 12x+6y+6z-42 = 0


⇒ 2x+y+z-7 = 0


The coordinates of the any point which lies on the line is


[(3-λ), (λ-4), (6λ-5)].


This point will also lie on the plane because the line crosses the plane. therefore, it will satisfy equation (2)-


2(3-λ) + (λ-4) + (6λ-5) - 7 = 0


⇒ 6-2λ+λ-4+6λ-5-7 = 0


⇒ 5λ-10 = 0


⇒ 5λ = 10


∴ λ = 2


Hence required coordinates are-


x = 1, y = -2, z = 7

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