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Question
The straight line \[\frac{x - 3}{3} = \frac{y - 2}{1} = \frac{z - 1}{0}\] is
Options
parallel to x-axis
parallel to y-axis
parallel to z-axis
perpendicular to z-axis
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Solution
perpendicular to z-axis
We have ,
\[\frac{x - 3}{3} = \frac{y - 2}{1} = \frac{z - 1}{0}\]
Also, the given line is parallel to the vector \[\vec{b} = 3 \hat{i} + \hat{j} + 0 \hat{k} \]
Let
\[x \hat{i} + y \hat{j} + z \hat{k} \] be perpendicular to the given line.
Now,
\[3x + 4y + 0z = 0\]
It is satisfied by the coordinates of z-axis, i.e.
(0, 0, 1).
Hence, the given line is perpendicular to z-axis.
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