Find the equation of the line passing through the point P (4, 6, 2) and the point of intersection of the line (x - 1)/3 = y/2 = (z + 1)/7

Question

Find the equation of the line passing through the point P (4, 6, 2) and the point of intersection of the line \(\frac{x-1}{3}=\frac{y}{2}=\frac{z+1}{7}\) and the plane x + y – z = 8.

Answer 1

Given line and plane are

\(\frac{x-1}{3}=\frac{y}{2}=\frac{z+1}{7}=\lambda\, .....(i)\)

and x + y + z = 8 ....(ii)

Let Q \((\alpha, \beta, \gamma)\) be point of intersection of equation (i) and (ii),

'Q' lie on line (i)

Also Q \((\alpha, \beta, \gamma)\) lie on plane (ii),

Required equation of line passing through P(4, 6, 2) and Q (-8, -6, -22) is