If left( frac{1}{2}, frac{1}{3}, n right) are | vedclass

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(A) The direction cosines $(l, m, n)$ of a line satisfy the condition $l^2 + m^2 + n^2 = 1$. Given the direction cosines are $\left( \frac{1}{2}, \fra

Vedclass · Accepted Answer

$\frac{\sqrt{23}}{6}$

Vedclass · Answer

(A) The direction cosines $(l, m, n)$ of a line satisfy the condition $l^2 + m^2 + n^2 = 1$. Given the direction cosines are $\left( \frac{1}{2}, \frac{1}{3}, n \right)$,we have: $\left( \frac{1}{2} \right)^2 + \left( \frac{1}{3} \right)^2 + n^2 = 1$ $\frac{1}{4} + \frac{1}{9} + n^2 = 1$ $\frac{9 + 4}{36} + n^2 = 1$ $\frac{13}{36} + n^2 = 1$ $n^2 = 1 - \frac{13}{36}$ $n^2 = \frac{36 - 13}{36} = \frac{23}{36}$ $n = \pm \frac{\sqrt{23}}{6}$. Since the option provided is positive,the correct value is $\frac{\sqrt{23}}{6}$.

If $\left( \frac{1}{2}, \frac{1}{3}, n \right)$ are the direction cosines of a line,then the value of $n$ is

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