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

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Solution

We know if $l, m, n$ are the direction cosines of any line then $l^{2} + m^{2} + n^{2} = 1$ .

But here $1^{2} + 1^{2} + 1^{2} = 3 \neq 1$ .

So $1, 1, 1$ can't be the direction cosines for any line.

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