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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