(B) The direction cosines of a line are denoted by $l, m, n$. We know that for any line,the sum of the squares of its direction cosines is always equa

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(B) The direction cosines of a line are denoted by $l, m, n$. We know that for any line,the sum of the squares of its direction cosines is always equal to $1$,i.e.,$l^2 + m^2 + n^2 = 1$. Given the direction cosines are $\left(\frac{1}{c}, \frac{1}{c}, \frac{1}{c}\right)$. Substituting these values into the identity: $\left(\frac{1}{c}\right)^2 + \left(\frac{1}{c}\right)^2 + \left(\frac{1}{c}\right)^2 = 1$ $\frac{1}{c^2} + \frac{1}{c^2} + \frac{1}{c^2} = 1$ $\frac{3}{c^2} = 1$ $c^2 = 3$ $c = \pm \sqrt{3}$

Class 12 Mathematics THREE DIMENSIONAL GEOMETRY System of co-ordinates, Direction cosines and direction ratios, Projection

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If the direction cosines of a straight line are $\left(\frac{1}{c}, \frac{1}{c}, \frac{1}{c}\right)$,then $c$ is equal to

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A
$\pm \sqrt{2}$
B
$\pm \sqrt{3}$
C
$\pm 2$
D
$\pm 3$

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THREE DIMENSIONAL GEOMETRY

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System of co-ordinates, Direction cosines and direction ratios, Projection

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$A$ line makes the same angle $\theta$ with each of the $x$ and $z$ axes. If the angle $\beta$ which it makes with the $y$-axis is such that $\sin^2 \beta = 3\sin^2 \theta$,then $\cos^2 \theta$ is-

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If the direction cosines of a straight line are $\left(\frac{1}{c}, \frac{1}{c}, \frac{1}{c}\right)$,then $c$ is equal to

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