The straight line \(\displaystyle\frac{x + 3}{3} = \frac{y + 2}{4} = \frac{z + 1}{0}\) is
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → Perpendicular to \(z\)-axis
The denominators give the direction ratios of the line: 3, 4, 0. A zero denominator only means that z does not change along the line (here \(z = -1\) throughout).
The z-axis has direction ratios 0, 0, 1. Two lines are perpendicular when \(a_1a_2 + b_1b_2 + c_1c_2 = 0\):
\(3(0) + 4(0) + 0(1) = 0\)
So the line is perpendicular to the z-axis.
It is not parallel to any axis: that would need direction ratios proportional to 1, 0, 0 or 0, 1, 0 or 0, 0, 1, but 3, 4, 0 has two non-zero entries.