Question

Determine an equation of the line that passes through the point P(5,-2,3) and is parallel to the line of the intersection of planes π₁: x+2y-z=6 and π₂: y+2z=1

Answer 1

Given: The equation of two planes and a point

To Determine: The equation of the line that passes through the point and parallel to the intersecting plane

Solution

`\begin{gathered} \pi_`:x+2y-z=6 \\ \pi_2:y+2z=1 \\ from\pi_1 \\ z+2y-z=6 \\ x+2y-6=z \end{gathered}`

Substitute for z in 2