If the direction ratios of two lines are a_1, | vedclass

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(C) Two lines with direction ratios $(a_1, b_1, c_1)$ and $(a_2, b_2, c_2)$ are parallel if and only if their direction ratios are proportional.Mathem

Vedclass · Accepted Answer

$\frac{a_1}{a_2} = \frac{b_1}{b_2} = \frac{c_1}{c_2}$

Vedclass · Answer

(C) Two lines with direction ratios $(a_1, b_1, c_1)$ and $(a_2, b_2, c_2)$ are parallel if and only if their direction ratios are proportional.Mathematically,this condition is expressed as:$\frac{a_1}{a_2} = \frac{b_1}{b_2} = \frac{c_1}{c_2} = k$where $k$ is a non-zero constant.This implies that the direction vectors of the two lines,$\vec{v_1} = a_1\hat{i} + b_1\hat{j} + c_1\hat{k}$ and $\vec{v_2} = a_2\hat{i} + b_2\hat{j} + c_2\hat{k}$,are collinear,meaning $\vec{v_1} = k\vec{v_2}$.Therefore,the correct condition for the lines to be parallel is $\frac{a_1}{a_2} = \frac{b_1}{b_2} = \frac{c_1}{c_2}$.

If the direction ratios of two lines are $a_1, b_1, c_1$ and $a_2, b_2, c_2$,then when are these lines parallel?

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