The equation $\frac{3 x + 1}{2} = \frac{y - 1}{2} = \frac{- z + 5}{3}$ represents a straight line. Obtain a set of direction ratios for the straight line.

- 2 : 3 : 9

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2 : 6 : - 9

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2 : - 6 : 9

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2 : - 3 : 9

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Solution

The correct option is B $2 : 6 : - 9$
given equation is

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

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

By comparing with a standard formula

$a = \frac{2}{3}$

$b = 2$

$c = - 3$

direction ratios of line = $3 \times \frac{2}{3}, 3 \times 2, - 3 \times 3$

direction ratios of line = $2, 6, - 9$

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

\frac{x - 3}{4} = \frac{y - 2}{2} = \frac{z - 6}{3}

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

Find the separate equations of pair of straight lines $y^{2} - 9 x y + 10 x^{2} = 0$

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