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

Question

Philoid · Accepted Answer

Here, l = 1, m = 1, n = 1

And, we know that –

l² + m² + n² = 1

Taking LHS,

l² + m² + n² = (1)² + (1)² + (1)²

= 3

≠1

⇒ LHS≠RHS

∴ 1, 1, and 1 cannot be direction cosines of a straight line.