The direction cosines of the vector hat{i} + | vedclass

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(C) The direction cosines of a vector $\vec{A} = a\hat{i} + b\hat{j} + c\hat{k}$ are given by the formula:$l = \frac{a}{|\vec{A}|}, m = \frac{b}{|\vec

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$\frac{1}{2}, \frac{1}{2}, \frac{1}{\sqrt{2}}$

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(C) The direction cosines of a vector $\vec{A} = a\hat{i} + b\hat{j} + c\hat{k}$ are given by the formula:$l = \frac{a}{|\vec{A}|}, m = \frac{b}{|\vec{A}|}, n = \frac{c}{|\vec{A}|}$where $|\vec{A}| = \sqrt{a^2 + b^2 + c^2}$.For the given vector $\vec{A} = 1\hat{i} + 1\hat{j} + \sqrt{2}\hat{k}$,the magnitude is:$|\vec{A}| = \sqrt{1^2 + 1^2 + (\sqrt{2})^2} = \sqrt{1 + 1 + 2} = \sqrt{4} = 2$.Now,calculating the direction cosines:$l = \frac{1}{2}$$m = \frac{1}{2}$$n = \frac{\sqrt{2}}{2} = \frac{1}{\sqrt{2}}$Thus,the direction cosines are $\frac{1}{2}, \frac{1}{2}, \frac{1}{\sqrt{2}}$.

The direction cosines of the vector $\hat{i} + \hat{j} + \sqrt{2}\hat{k}$ are:

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