If the direction ratios of two parallel lines $4, - 3, - 1$ and $p + q, 1 + q, 2$ then find the values of $p$ and $q$ .

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Solution

Since lines are parallel, so $\frac{4}{p + q} = \frac{- 3}{p + q} = \frac{- 1}{2} \frac{- 3}{1 + q} = \frac{- 1}{2} 6 = 1 + q ⟹ q = 5$

and $\frac{4}{p + q} = \frac{- 1}{2}$
$- 8 = p + q ⟹ p = - 8 - q = - 8 - 5 = - 13$

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