The straight line (x + 3)/3 = (y + 2)/4 = (z + 1)/0 is

The correct answer is Option (4) → Perpendicular to z-axis

Given line: $\displaystyle \frac{x + 3}{3} = \frac{y + 2}{4} = \frac{z + 1}{0}$

Since $\displaystyle \frac{z + 1}{0}$ is undefined, it implies $z + 1 = 0 \Rightarrow z = -1$

So the line lies entirely in the plane $z = -1$, i.e., it does not vary along the $z$-axis

Direction ratios of the line: $(3, 4, 0)$

This means the line is parallel to the vector $3\hat{i} + 4\hat{j}$ and has no $k$ component

⟹ The line lies in the $xy$-plane and is perpendicular to the $z$-axis