The direction cosines of z-axis are:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 0, 0, 1
The direction cosines of a line are the cosines of the angles it makes with the x-, y- and z-axes.
The z-axis makes angles 90°, 90° and 0° with the three axes, so its direction cosines are
\(\cos 90^\circ,\ \cos 90^\circ,\ \cos 0^\circ\)
\(= 0,\ 0,\ 1\)
Why the other options are incorrect
Option (1) 1, 0, 0 — Incorrect. These are the direction cosines of the x-axis.
Option (2) 0, 1, 0 — Incorrect. These are the direction cosines of the y-axis.
Option (4) 1, 1, 1 — Incorrect. Direction cosines satisfy \(l^2 + m^2 + n^2 = 1\), but here the sum of squares is 3.
NCERT (2026-27 edition):
Direction Cosines and Direction Ratios of a Line
