UPSC NDA Math Model Paper 9

Given:
Direction cosines of a line are (1/p, 1/p, 1/p)
So, l = 1/p, m = 1/p and n = 1/p
We know that sum of squares of the direction cosines of a line is equal to unity
⇒l2+m2+n2=1
⇒(1∕p2)+(1∕p2)+(1∕p2)=1
⇒3∕p2=1
⇒p2=3
∴p=±√3