The equation of a line passing through the po | vedclass

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Question

(C) The equation of a line passing through a point $(x_1, y_1, z_1)$ and having direction ratios $(a, b, c)$ is given by $\frac{x - x_1}{a} = \frac{y

Vedclass · Accepted Answer

$\frac{x - 2}{2} = \frac{y + 1}{7} = \frac{z - 1}{-3}$

Vedclass · Answer

(C) The equation of a line passing through a point $(x_1, y_1, z_1)$ and having direction ratios $(a, b, c)$ is given by $\frac{x - x_1}{a} = \frac{y - y_1}{b} = \frac{z - z_1}{c}$.Given that the line passes through the point $(2, -1, 1)$,we have $x_1 = 2, y_1 = -1, z_1 = 1$.Since the required line is parallel to the line $\frac{x - 3}{2} = \frac{y + 1}{7} = \frac{z - 2}{-3}$,it will have the same direction ratios as the given line.Thus,the direction ratios are $a = 2, b = 7, c = -3$.Substituting these values into the standard equation,we get $\frac{x - 2}{2} = \frac{y - (-1)}{7} = \frac{z - 1}{-3}$,which simplifies to $\frac{x - 2}{2} = \frac{y + 1}{7} = \frac{z - 1}{-3}$.

The equation of a line passing through the point $(2, -1, 1)$ and parallel to the line whose equation is $\frac{x - 3}{2} = \frac{y + 1}{7} = \frac{z - 2}{-3}$ is:

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