Question
Find the vector equation for the line passing through the points (– 1, 0, 2) and (3, 4, 6).
Solution
The line passes through the points A(– 1, 0, 2), B(3, 4, 6).

where
are position vectors of A and B respectively.

Let
be the position vector of any point on the given line.
∴ the vector equation of line is

or

where


Let

∴ the vector equation of line is

or
