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Q.

If $e = l i + m j + n k$ is a unit vector then maximum value of 'lm + mn + nl' is____

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answer is 1.

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Detailed Solution

${(l - m)}^{2} + {(m - n)}^{2} + {(n - l)}^{2} \geq 0 \Rightarrow 2 l^{2} + 2 m^{2} + 2 n^{2} - 2 l m - 2 m n - 2 n l \geq 0 \Rightarrow 2 (l^{2} + m^{2} + n^{2}) - 2 (l m + m n + n l) \geq 0 \Rightarrow 2 - 2 (l m + m n + n l) \geq 0 \Rightarrow l m + m n + n l \leq 1$

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