Question

Prove that 1, 1, 1 cannot be direction cosines of a straight line.

Answer 1

Let 1, 1, 1 be the direction cosines of a straight line.
Then \[1^2 + 1^2 + 1^2 = 3\] 
Since direction cosines of a line which makes equal angle with the axes  must satisfy \[l^2 + m^2 + n^2 = 1\]
Hence 1, 1, 1 cannot be the direction cosines of a straight line.