Question

A line passes through the point with position vector $3\hat{i}-4\hat{j}+5\hat{k}$ and is in the direction of $\hat{i}+2\hat{j}-3\hat{k}$ find the equation of the line in vector and Cartesian from.

Answer 1

Passing through $(2,-6,5)$

Parallel to $\hat{i}+2\hat{i}-3k\Rightarrow$ dv $(1,2,-3)$

$\therefore$ equation $\frac{x-3}{1}=\frac{y+4}{2}=\frac{3-5}{-3}$