NDA 2018 Maths · Mathematics · Three Dimensional Geometry · easy

An acute-angled line makes angles 60^° and 45^° with the x-axis and y-axis. The angle it makes with the z-axis is

Single correct option

An acute-angled line makes angles

60^\circ

and

45^\circ

with the

x

-axis and

y

-axis. The angle it makes with the

z

-axis is

Show answer and solution

Answer: (D) $60^\circ$

With

l=\cos60^\circ=\frac12

and

m=\cos45^\circ=\frac1{\sqrt2}

, the relation

l^2+m^2+n^2=1

gives

n^2=1-\frac14-\frac12=\frac14

, so

n=\frac12

(acute) and the angle is

60^\circ

. The trap is to subtract the angles from

180^\circ

instead of using direction cosines.

Original question written in the NDA 2018 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