Q. 19

# Find the point where the line meets the plane 2x + 4y – z = 1.

Given :

Equation of plane : 2x + 4y - z = 1

Equation of line : To Find : Point of intersection of line and plane.

Let P(a, b, c) be point of intersection of plane and line.

As point P lies on the line, we can write, a = 2k+1, b = -3k+2, c = 4k-3 ………(1)

Also point P lies on the plane

2a + 4b – c = 1

2(2k+1) + 4(-3k+2) – (4k-3) = 1 …..from (1)

4k + 2 – 12k + 8 – 4k + 3 = 1

-12k = -12

k = 1 ,  Therefore, co-ordinates of point of intersection of given line and plane are

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Find the coordinate of the point P where the line through and crosses the plane passing through three points and Also, find the ratio in which P divides the line segment AB.

Mathematics - Board Papers