UPSC NDA I 2017 Mathematics Solved Paper

Concept:Direction cosines $l$, $m$, $n$ are the cosines of the angles $\alpha$, $\beta$, $\gamma$ that the line makes with the $x$‑, $y$‑, and $z$‑axes respectively.They satisfy $l^2 + m^2 + n^2 = 1$ and uniquely describe the line’s orientation in 3D space.Explanation:Given direction cosines are $\langle 0, 1, 0 \rangle$, so $l = 0$, $m = 1$, $n = 0$.$l = \cos \alpha = 0$ gives $\alpha = 90^\circ$ — the line is perpendicular to the $x$-axis.$m = \cos \beta = 1$ gives $\beta = 0^\circ$ — the line lies exactly along the $y$-axis.$n = \cos \gamma = 0$ gives $\gamma = 90^\circ$ — the line is perpendicular to the $z$-axis.Thus the line makes a $0^\circ$ angle with the $y$-axis; it is parallel to the $y$-axis.Answer:B. parallel to $y$-axis