(A) Given direction ratios are $a = 1$,$b = -3$,and $c = 2$. The magnitude of the vector is $\sqrt{a^2 + b^2 + c^2} = \sqrt{1^2 + (-3)^2 + 2^2} = \sqr

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$\frac{1}{\sqrt{14}}, \frac{-3}{\sqrt{14}}, \frac{2}{\sqrt{14}}$

(A) Given direction ratios are $a = 1$,$b = -3$,and $c = 2$. The magnitude of the vector is $\sqrt{a^2 + b^2 + c^2} = \sqrt{1^2 + (-3)^2 + 2^2} = \sqrt{1 + 9 + 4} = \sqrt{14}$. The direction cosines $(l, m, n)$ are given by $\frac{a}{\sqrt{a^2 + b^2 + c^2}}, \frac{b}{\sqrt{a^2 + b^2 + c^2}}, \frac{c}{\sqrt{a^2 + b^2 + c^2}}$. Substituting the values,we get $\left( \frac{1}{\sqrt{14}}, \frac{-3}{\sqrt{14}}, \frac{2}{\sqrt{14}} \right)$.

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

Easy

If the direction ratios of a line are $1, -3, 2$,then the direction cosines of the line are

A
$\frac{1}{\sqrt{14}}, \frac{-3}{\sqrt{14}}, \frac{2}{\sqrt{14}}$
B
$\frac{1}{\sqrt{14}}, \frac{2}{\sqrt{14}}, \frac{3}{\sqrt{14}}$
C
$\frac{-1}{\sqrt{14}}, \frac{3}{\sqrt{14}}, \frac{-2}{\sqrt{14}}$
D
$\frac{-1}{\sqrt{14}}, \frac{-2}{\sqrt{14}}, \frac{-3}{\sqrt{14}}$

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THREE DIMENSIONAL GEOMETRY

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

The angle between the lines whose direction cosines $(\ell, m, n)$ satisfy the equations $\ell+m+n=0$ and $\ell^2+m^2-n^2=0$ is:

MediumMHT CET 2025

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If the direction ratios of a line are $1, -3, 2$,find the direction cosines of the line.

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The direction cosines $\ell, m, n$ of the line $\frac{x+2}{2}=\frac{2y-4}{3}; z=-1$ are:

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Each of the angles $\beta$ and $\gamma$ that a given line makes with the positive $y-$ and $z-$axes,respectively,is half of the angle that this line makes with the positive $x-$axis. Then the sum of all possible values of the angle $\beta$ is

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If the line with direction ratios $(1, \alpha, \beta)$ is perpendicular to the line with direction ratios $(-1, 2, 1)$ and parallel to the line with direction ratios $(\alpha, 1, \beta)$,then $(\alpha, \beta)$ is

EasyAP EAMCET 2024

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If the direction ratios of a line are $1, -3, 2$,then the direction cosines of the line are

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