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