What is the equation of the line passing thro | vedclass

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(D) The equation of a line passing through the point $(a, b, c)$ is given by $\frac{x - a}{l} = \frac{y - b}{m} = \frac{z - c}{n}$,where $(l, m, n)$ a

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$\frac{x - a}{0} = \frac{y - b}{0} = \frac{z - c}{1}$

Vedclass · Answer

(D) The equation of a line passing through the point $(a, b, c)$ is given by $\frac{x - a}{l} = \frac{y - b}{m} = \frac{z - c}{n}$,where $(l, m, n)$ are the direction ratios of the line.Since the line is parallel to the $z$-axis,its direction ratios must be proportional to the direction ratios of the $z$-axis,which are $(0, 0, 1)$.Therefore,we can take $l = 0$,$m = 0$,and $n = 1$.Substituting these values into the standard equation,we get $\frac{x - a}{0} = \frac{y - b}{0} = \frac{z - c}{1}$.

What is the equation of the line passing through the point $(a, b, c)$ and parallel to the $z$-axis?

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