The equation of straight line passing through the point(a, b, c) and parallel to z- axis, is
[MP PET 1995; Pb. CET 2000]

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Solution

The correct option is D

The line through (a,b,c) is $\frac{x - a}{l} = \frac{y - b}{m} = \frac{z - c}{n}$ ....(i)
Since the line is parallel to z-axis, therefore any point on this line will be of the form $(a, b, z_{1})$ .
Also any point on line (i) is $(l r + a, m r + b, n r + c)$ .
Hence $\begin{matrix} l r + a + = a m r + b = b \end{matrix}$ $\Rightarrow l = m = 0$
Hence the line will be $\frac{x - a}{0} = \frac{y - b}{0} = \frac{z - c}{1}$ .

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