Find the equation

Given: line passes through (-1, 3, -2) 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 a₁:a₂:a₃ and b₁:b₂:b₃ are perpendicular, then a₁b₁+a₂b₂+a₃b₃ = 0

Explanation:

Here,

Let the direction ratios of the line be b₁:b₂:b₃

Direction ratios of the other two lines are 1 : 2 : 3 and -3 : 2 : 5

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

b₁ + 2b₂ + 3b₃ = 0

-3b₁ + 2b₂ + 5b₃ = 0

Solving,

Therefore,

Vector form of the line is:

Cartesian form of the line is: