Find the equations of the line passing through the point and perpendicular to each of the lines and

Answer

Given: line passes through and is perpendicular to each of the lines and

To find: equation of line in Vector and Cartesian form

Formula Used: Equation of a line is

Vector form:

Cartesian form: .

where is a point on the line and is a vector parallel to the line.

If 2 lines of direction ratios and are perpendicular, then

Explanation:

Here,

Let the direction ratios of the line be

Direction ratios of the other two lines are and

Since the other two line are perpendicular to the given line, we have

Solving,