Direction ratios of two lines are a, b, c and | vedclass

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(B) Let the direction ratios of the first line be $l_1, m_1, n_1 = a, b, c$.Let the direction ratios of the second line be $l_2, m_2, n_2 = \frac{1}{b

Vedclass · Accepted Answer

Parallel

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(B) Let the direction ratios of the first line be $l_1, m_1, n_1 = a, b, c$.Let the direction ratios of the second line be $l_2, m_2, n_2 = \frac{1}{bc}, \frac{1}{ca}, \frac{1}{ab}$.Two lines are parallel if their direction ratios are proportional,i.e.,$\frac{l_1}{l_2} = \frac{m_1}{m_2} = \frac{n_1}{n_2}$.Calculating the ratios:$\frac{a}{1/bc} = a 	imes bc = abc$$\frac{b}{1/ca} = b 	imes ca = abc$$\frac{c}{1/ab} = c 	imes ab = abc$Since $\frac{a}{1/bc} = \frac{b}{1/ca} = \frac{c}{1/ab} = abc$,the direction ratios are proportional.Therefore,the lines are parallel.

Direction ratios of two lines are $a, b, c$ and $\frac{1}{bc}, \frac{1}{ca}, \frac{1}{ab}$. The lines are

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