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

Solution:

The vector eq. of a line passing through a point with position vector and parallel to vector is given as

Given that the line passes through
Therefore,
Let’s find the normal of plane

Now compare it with

As line is perpendicular to plane, the line will be parallel of the plane

Therefore,

As a resullt, the required vector equation of line is