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

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

Vedclass · Answer

(A) The equation of a line passing through $(x_1, y_1, z_1)$ with 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 $(-3, 2, -5)$,we have $x_1 = -3, y_1 = 2, z_1 = -5$.Since the line is equally inclined to the positive coordinate axes,the direction cosines $(l, m, n)$ are equal,i.e.,$l = m = n$.Thus,the direction ratios can be taken as $a = 1, b = 1, c = 1$.Substituting these values into the equation,we get $\frac{x - (-3)}{1} = \frac{y - 2}{1} = \frac{z - (-5)}{1}$.Therefore,the equation of the line is $\frac{x+3}{1} = \frac{y-2}{1} = \frac{z+5}{1}$.

The equation of the line equally inclined with the positive coordinate axes and passing through $(-3, 2, -5)$ is

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