Find the direction cosines of the vector hat{ | vedclass

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(A) Let the vector be $\vec{a} = \hat{i} + 2\hat{j} + 3\hat{k}$.The magnitude of the vector is given by $|\vec{a}| = \sqrt{1^2 + 2^2 + 3^2} = \sqrt{1

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$\left(\frac{1}{\sqrt{14}}, \frac{2}{\sqrt{14}}, \frac{3}{\sqrt{14}}\right)$

Vedclass · Answer

(A) Let the vector be $\vec{a} = \hat{i} + 2\hat{j} + 3\hat{k}$.The magnitude of the vector is given by $|\vec{a}| = \sqrt{1^2 + 2^2 + 3^2} = \sqrt{1 + 4 + 9} = \sqrt{14}$.The direction cosines $(l, m, n)$ of a vector $a\hat{i} + b\hat{j} + c\hat{k}$ are given by $\left(\frac{a}{|\vec{a}|}, \frac{b}{|\vec{a}|}, \frac{c}{|\vec{a}|}\right)$.Substituting the values,we get the direction cosines as $\left(\frac{1}{\sqrt{14}}, \frac{2}{\sqrt{14}}, \frac{3}{\sqrt{14}}\right)$.

Find the direction cosines of the vector $\hat{i}+2 \hat{j}+3 \hat{k}$.

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