Question

Find the vector equation of the line passing through (1, 2, 3) and parallel to the planes

vector r= (i-j+2k) =5 and vector r.(3i+j+k)=6

Answer 1

Let the required line be parallel to vector b given by,

The line in equation (1) and plane in equation (2) are parallel. Therefore, the normal to the plane of equation (2) and the given line are perpendicular.

This is the equation of the required line.