The direction cosines of a line satisfy the relation: l2+m2+n2=1,
where l,m,n are the direction cosines.
Here: l=3k,m=3k,n=3k.
Substitute into the equation: (3k)2+(3k)2+(3k)2=1.
Simplify: 3k2+3k2+3k2=1⟹9k2=1⟹k2=91. Thus: k=±31.
The correct answer is (D) ±31.