Prove that 1, 1, 1 cannot be direction cosines of a straight line… - Vidyadip

Question

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

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Answer

Let 1, 1, 1 be the direction cosines of a straight line. Then,
$1^2+1^2+1^2=3\neq1$
Since direction cosines of a line which makes equal angle with the axes must satisfy
$\text{l}^2+\text{m}^2+\text{n}^2=1$
Hence 1, 1, 1 cannot be the direction cosines of a straight line.

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