Linear Algebra, Vectors

Question

Find equation of a line passes through the points = (0, 1, 2) and = (-1, 1, 1).

Comments

Refer the above image.

Suppose $P_1$ and $P_2$ are A and B here. So, co-ordinates of C here are $(-1,1,1) \  –  \  (0,1,2) = (-1,0,-1)$

This line OC is parallel to line AB. Hence, equation of the line passing through A (which is P1)  and B (which is P2) here is:

$x= (0,1,2) + t(-1,0,-1),$ where $t$ is any real number.