# Find the equation of the line passing through the point P(4, 6, 2) and the point of intersection of the line and the plane x + y –Z = 8.

Given :

Equation of plane : x + y - z = 8

Equation of line :

Point : P = (4, 6, 2)

To Find : Equation of line.

Formula :

Equation of line passing through A = (x1, y1, z1) &

B = (x2, y2, z2) is

let Q (a, b, c) be point of intersection of plane and line.

As point Q lies on the line, we can write,

a =3k+1, b= 2k, c= 7k-1

Also point Q lies on the plane,

a + b – c = 8

(3k+1) + (2k) – (7k-1) = 8

3k + 1 + 2k – 7k + 1 = 8

-2k = 6

k = -3

,

Therefore, co-ordinates of point of intersection of given line and plane are Q = (-8, -6, -22)

Now, equation of line passing through P(4,6,2) and

Q(-8, -6, -22) is

This is the equation of required line

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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