PrepRung
Sign inSign up free

NDA 2017 Maths · Mathematics · Three Dimensional Geometry · medium

A line makes an angle of 60^° with each of the x-axis and y-axis and an acute angle γ with the z-axis. Then γ equals

Single correct option

A line makes an angle of 60∘60^\circ with each of the xx-axis and yy-axis and an acute angle γ\gamma with the zz-axis. Then γ\gamma equals
  1. A. 30∘30^\circ
  2. B. 60∘60^\circ
  3. C. 45∘45^\circ
  4. D. 90∘90^\circ
Show answer and solution

Answer: (C) 45∘45^\circ

Direction cosines satisfy cos⁡2α+cos⁡2β+cos⁡2γ=1\cos^2\alpha+\cos^2\beta+\cos^2\gamma=1, so 14+14+cos⁡2γ=1\frac14+\frac14+\cos^2\gamma=1, giving cos⁡2γ=12\cos^2\gamma=\frac12 and γ=45∘\gamma=45^\circ. Choosing 60∘60^\circ assumes equal inclination to all three axes, which would need cos⁡2γ=14\cos^2\gamma=\frac14 and fails the identity.
Report a mistake

Original question written in the NDA 2017 Maths pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake