Question

Cartestion equation of a line $PQ$ is
$\frac{3x+2}{5}=\frac{4-3y}{6}=\frac{6-z}{2}$. Then the direction ratios of the line parallel to $PQ$ are _______

Answer 1

$\frac{3x+2}{5}=\frac{4-3y}{6}=\frac{6-z}{2}$
Equation of line can be rewritten as
$\frac{x+\frac{2}{3}}{\frac{5}{3}}=\frac{y-\frac{4}{3}}{-2}=\frac{z-6}{-2}$
Direction ratios of the line $PQ$ are $(\frac{5}{3},-2,-2)$
Therefore, the direction ratios of line parallel to $PQ$ are $(\frac{5k}{3},-2k,-2k)$, where $k\in R$.