(A) The direction cosines of a line that makes angles $\alpha, \beta, \gamma$ with the positive $x, y, z$-axes are given by $l = \cos \alpha$,$m = \co

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$\left(\frac{\sqrt{3}}{2}, \frac{1}{2}, 0\right)$

(A) The direction cosines of a line that makes angles $\alpha, \beta, \gamma$ with the positive $x, y, z$-axes are given by $l = \cos \alpha$,$m = \cos \beta$,and $n = \cos \gamma$.Given $\alpha = 30^{\circ}$,$\beta = 60^{\circ}$,and $\gamma = 90^{\circ}$.Thus,the direction cosines are:$l = \cos 30^{\circ} = \frac{\sqrt{3}}{2}$$m = \cos 60^{\circ} = \frac{1}{2}$$n = \cos 90^{\circ} = 0$Therefore,the direction cosines are $\left(\frac{\sqrt{3}}{2}, \frac{1}{2}, 0\right)$.

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

Easy

If a line makes an angle of $30^{\circ}, 60^{\circ}, 90^{\circ}$ with the positive direction of $x, y, z$-axes,respectively,then find its direction cosines.

A
$\left(\frac{\sqrt{3}}{2}, \frac{1}{2}, 0\right)$
B
$\left(\frac{1}{2}, \frac{\sqrt{3}}{2}, 0\right)$
C
$\left(\frac{\sqrt{3}}{2}, 0, \frac{1}{2}\right)$
D
$\left(0, \frac{1}{2}, \frac{\sqrt{3}}{2}\right)$

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THREE DIMENSIONAL GEOMETRY

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

Find the octants in which the points $(-3, 1, 2)$ and $(-3, 1, -2)$ lie.

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If $\alpha, \beta, \gamma$ are the angles made by a line with the positive directions of the $x, y, z$ axes respectively,then $\sin^2 \alpha + \sin^2 \beta + \sin^2 \gamma = \dots$

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$A$ line which makes an angle of $60^o$ with the $y$-axis and $z$-axis,then the angle which it makes with the $x$-axis is ......... $^o$.

Easy

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Let $A(1,-1,2), B(6,11,2), C(1,2,6)$ be three points. If $l_1, m_1, n_1$ are the direction cosines of $AB$ and $l_2, m_2, n_2$ are the direction cosines of $AC$,then $|l_1 l_2+m_1 m_2+n_1 n_2|=$

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If $OP = 8$ and $\overrightarrow{OP}$ makes angles $45^\circ$ and $60^\circ$ with the $OX$-axis and $OY$-axis respectively,then $\overrightarrow{OP} = $

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If a line makes an angle of $30^{\circ}, 60^{\circ}, 90^{\circ}$ with the positive direction of $x, y, z$-axes,respectively,then find its direction cosines.

Similar Questions

Find the octants in which the points $(-3, 1, 2)$ and $(-3, 1, -2)$ lie.

If $\alpha, \beta, \gamma$ are the angles made by a line with the positive directions of the $x, y, z$ axes respectively,then $\sin^2 \alpha + \sin^2 \beta + \sin^2 \gamma = \dots$

$A$ line which makes an angle of $60^o$ with the $y$-axis and $z$-axis,then the angle which it makes with the $x$-axis is ......... $^o$.

Let $A(1,-1,2), B(6,11,2), C(1,2,6)$ be three points. If $l_1, m_1, n_1$ are the direction cosines of $AB$ and $l_2, m_2, n_2$ are the direction cosines of $AC$,then $|l_1 l_2+m_1 m_2+n_1 n_2|=$

If $OP = 8$ and $\overrightarrow{OP}$ makes angles $45^\circ$ and $60^\circ$ with the $OX$-axis and $OY$-axis respectively,then $\overrightarrow{OP} = $

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