Write the vector equation of the line passing through the point (1, –2, –3) and normal to the plane .

Equation of the given plane is,

So, the equation of the vector normal to the plane is given as,

As the required line should be normal to the given plane, so, the line should be parallel to the normal vector i.e. .

The line should pass through the point (1, –2, –3).

We can write the position vector of the point as,

So, the vector equation of the line passing through the point (1, –2, –3) and normal to the plane i.e. parallel to is given by,

, where is a scalar(constant).

Hence, equation of the required line is

where, is a scalar(constant)