Q. 105.0( 2 Votes )

# Find the equation of the plane through the line of intersection of the planes and , which is at a unit distance from the origin?

and

x + 3y + 6 = 0 and 3x – y – 4z = 0

x + 3y + 6 + k(3x – y – 4z) = 0

x(1 + 3k) + y(3 – k) – 4zk + 6 = 0

Distance from origin to plane =

36 = (1 + 3k)2 + (3 – k)2 + (4k)2

36 = 1 + 6k + 9k2 + 9 – 6k + k2 + 16k2

26 = 26k2

k2 = 1

k = 1

case :1 k = 1

x + 3y + 6 + 1(3x – y – 4z) = 0

4x + 2y – 4z + 6 = 0

Case :2 k = – 1

x + 3y + 6 – 1(3x – y – 4z) = 0

2x – 4y – 4z – 6 = 0

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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.

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