Question

Write the equation of the line passing through $(2,-6,3)$ & having D.R.'s $\propto$ $1,5,9$.

Answer 1

The line passes through the points $(2,-6,3)$

and direction ratios $(1,5,9)$

If line passing through the point $(a,b,c)$ and having direction ratios $(p,q,r)$ then the equation of line will be,

$\frac{x-a}{p}=\frac{y-b}{q}=\frac{z-c}{r}$

From above data, equation will be;

$\frac{x-2}{1}=\frac{y+6}{5}=\frac{z-3}{9}$

$\Rightarrow 45(x-2)=45\left(\frac{y+6}{5}\right)=45\left(\frac{z-3}{9}\right)$

$\Rightarrow 45x-90=9y+54=5z-15$