If $\frac{1}{2}, \frac{1}{3}, n$ are the direction cosines of a line, then the values of n are ________________.

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Solution

Let us suppose, $l = \frac{1}{2}, m = \frac{1}{3}$ and n = n are the direction cosines of a line then l² + m² + n²= 1
$i . e {(\frac{1}{2})}^{2} + {(\frac{1}{3})}^{2} + n^{2} = 1 i . e \frac{1}{4} + \frac{1}{9} + n^{2} = 1 i . e n^{2} = 1 - \frac{1}{4} - \frac{1}{9} i . e n^{2} = \frac{36 - 9 - 4}{36} i . e n^{2} = \frac{23}{36} i . e n = \pm \frac{\sqrt{23}}{6} i . e n = \pm \frac{\sqrt{23}}{6}$

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