The equation of the line that passes through | vedclass

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Question

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

Vedclass · Accepted Answer

$\frac{x}{1}=\frac{y}{0}=\frac{z}{0}$

Vedclass · Answer

(D) The equation of a line passing through a point $(x_1, y_1, z_1)$ with direction ratios $(a, b, c)$ is given by $\frac{x-x_1}{a} = \frac{y-y_1}{b} = \frac{z-z_1}{c}$.Since the line passes through the origin,$(x_1, y_1, z_1) = (0, 0, 0)$.Since the line is parallel to the $X$-axis,its direction ratios are proportional to $(1, 0, 0)$,so $(a, b, c) = (1, 0, 0)$.Substituting these values into the equation,we get $\frac{x-0}{1} = \frac{y-0}{0} = \frac{z-0}{0}$,which simplifies to $\frac{x}{1} = \frac{y}{0} = \frac{z}{0}$.Therefore,the correct option is $D$.

The equation of the line that passes through the origin and is parallel to the $X$-axis is . . . . . . .

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