Question

Find the vector and cartesian equations of the line passing through the point (2, 1, 3) and perpendicular to the lines \(\frac{x-1}{1}=\frac{y-2}{2}=\frac{z-3}{3}\) and \(\frac{x}{-3}=\frac{y}{2}=\frac{z}{5}.\)

Answer 1

Let the cartesian equation of the line passing through (2, 1, 3) be

Since, line (i) is perpendicular to given line

From equation (iv) and (v).

which is the cartesian form

The vector form is