Find the vector and Cartesian equations of the line passing through the points A(2, -3, 0) and B(-2, 4, 3).

Given: line passes through the points (2, -3, 0) and (-2, 4, 3)

To find: equation of line in vector and Cartesian forms

Formula Used: Equation of a line is

Vector form:

Cartesian form:

where is a point on the line and with b₁ : b₂ : b₃ being the direction ratios of the line.

Explanation:

Here,

The direction ratios of the line are (2 + 2) : (-3 - 4) : (0 - 3)

⇒ 4 : -7 : -3

⇒ -4 : 7 : 3

So,

Therefore,

Vector form:

Cartesian form: