(A) Let the vector be $\vec{a} = \hat{i} + \hat{j} - 2\hat{k}$.Its direction ratios are $(a, b, c) = (1, 1, -2)$.The magnitude of the vector is $|\vec

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$\left(\frac{1}{\sqrt{6}}, \frac{1}{\sqrt{6}}, \frac{-2}{\sqrt{6}}\right)$

(A) Let the vector be $\vec{a} = \hat{i} + \hat{j} - 2\hat{k}$.Its direction ratios are $(a, b, c) = (1, 1, -2)$.The magnitude of the vector is $|\vec{a}| = \sqrt{1^2 + 1^2 + (-2)^2} = \sqrt{1 + 1 + 4} = \sqrt{6}$.The direction cosines $(l, m, n)$ are given by $\left(\frac{a}{|\vec{a}|}, \frac{b}{|\vec{a}|}, \frac{c}{|\vec{a}|}\right)$.Substituting the values, we get $\left(\frac{1}{\sqrt{6}}, \frac{1}{\sqrt{6}}, \frac{-2}{\sqrt{6}}\right)$.

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

Easy

The direction cosines of the supporting line of the vector $\hat{i}+\hat{j}-2 \hat{k}$ are

TS EAMCET 2021 All TS EAMCET

A
$\left(\frac{1}{\sqrt{6}}, \frac{1}{\sqrt{6}}, \frac{-2}{\sqrt{6}}\right)$
B
$\left(\frac{1}{2}, \frac{1}{2},-1\right)$
C
$\left(\frac{1}{\sqrt{6}}, \frac{1}{\sqrt{6}}, \frac{2}{\sqrt{6}}\right)$
D
$\left(\frac{-1}{2}, \frac{-1}{2},-1\right)$

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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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The direction cosines of the supporting line of the vector $\hat{i}+\hat{j}-2 \hat{k}$ are

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