Find the equations of the line passing through the point (1, -2, 3) and parallel to the line Also find the vector form of this equation so obtained.

Given: line passes through (1, -2, 3) and is parallel to the line

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.

Explanation:

Since the line (say L₁) is parallel to another line (say L₂), L₁ has the same direction ratios as that of L₂

Here,

Since the equation of L₂ is

Therefore,

Vector form of the line is:

Cartesian form of the line is: