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

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

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

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

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

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Solution

The correct option is C $\frac{x - a}{0} = \frac{y - b}{0} = \frac{z - c}{1}$
The direction cosines of line parallel to $z$ -axis are $(0, 0, 1)$ .
Since, the line passes through $(a, b, c)$
Thus, its equation is $\frac{x - a}{0} = \frac{y - b}{0} = \frac{z - c}{1} .$
Hence, option B is correct.

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

The correct option is C x−a0=y−b0=z−c1The direction cosines of line parallel to z-axis are (0,0,1).Since, the line passes through (a,b,c)Thus, its equation is x−a0=y−b0=z−c1.Hence, option B is correct.

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

The correct option is C $\frac{x - a}{0} = \frac{y - b}{0} = \frac{z - c}{1}$
The direction cosines of line parallel to $z$ -axis are $(0, 0, 1)$ .
Since, the line passes through $(a, b, c)$
Thus, its equation is $\frac{x - a}{0} = \frac{y - b}{0} = \frac{z - c}{1} .$
Hence, option B is correct.