Question

The equation of the line is $2x-2=3y+1=6z-2$. Find its direction ratios and also, find the vector equation of line.

Answer 1

We have,

$2x-2=3y+1=6z-2$

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

Direction Ratios

$=(\frac{1}{2},\frac{1}{3},\frac{1}{6})$

Therefore, the vector equation

$=\hat{i}-\frac{1}{3}\hat{j}+\frac{1}{3}\hat{k}+\lambda (\frac{1}{2}\hat{i}+\frac{1}{3}\hat{j}+\frac{1}{6}\hat{k})$

$=\frac{3\hat{i}-\hat{j}+\hat{k}}{3}+\frac{\lambda }{6}(3\hat{i}+2\hat{j}+\hat{k})$

$=\hat{i}-\frac{\hat{j}}{3}+\frac{\hat{k}}{3}+\mu (3\hat{i}+2\hat{j}+\hat{k})$

Hence, this is the answer.