UPSC NDA Math Model Paper 4

Let l be the direction cosine along with x-axis, m be the direction cosine along the y-axis.
Therefore,
l=cos‌60°
=

1

2

Similarly,
m=cos‌30°
=

√3

2

We will substitute these values in (1).
l2+m2+n2=1
(

1

2

)2+(

√3

2

)2+n2=1

1

4

+

3

4

+n2=1
n2=0
n=0
Therefore, the angle made with the z-axis is cos inverse of 0.
We know that cos‌90°=0
Hence, the angle made with the z-axis is 90°.