Q20 of 230 Page 30

Find the coordinates of the point where the line intersects the plane x – y + z – 5 = 0. Also find the angle between the line and the plane.

Given line

Let


⇒ x = 3r + 2, y = 4r – 1, z = 2r + 2


Substituting in the equation of the plane x – y + z – 5 = 0


We get , (3r + 2) – (4r – 1) + (2r + 2) – 5 = 0


⇒ 3r + 2 – 4r + 1 + 2r + 2 – 5 = 0


⇒ r = 0


∴ x = 3×0 + 2, y = 4×0 – 1 , z = 2×0 + 2


⇒ x = 2, y = – 1, z = 2


Direction ratios of the line are 3, 4, 2


Direction ratios of the line perpendicular to the plane are 1, – 1, 1


∴


⇒


⇒


⇒ sinθ = ⇒ θ = sin – 1(


∴ the angle between the plane and the line is sin – 1(


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