If bar{a} = hat{i} + hat{j} + hat{k},bar{b} = | vedclass

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(A) Let $\bar{v} = 2\bar{a} - \bar{b} + 3\bar{c}$.Substituting the given vectors:$\bar{v} = 2(\hat{i} + \hat{j} + \hat{k}) - (4\hat{i} - 2\hat{j} + 3\

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$2\hat{i} - 4\hat{j} + 4\hat{k}$

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(A) Let $\bar{v} = 2\bar{a} - \bar{b} + 3\bar{c}$.Substituting the given vectors:$\bar{v} = 2(\hat{i} + \hat{j} + \hat{k}) - (4\hat{i} - 2\hat{j} + 3\hat{k}) + 3(\hat{i} - 2\hat{j} + \hat{k})$$\bar{v} = (2 - 4 + 3)\hat{i} + (2 + 2 - 6)\hat{j} + (2 - 3 + 3)\hat{k}$$\bar{v} = \hat{i} - 2\hat{j} + 2\hat{k}$The magnitude of $\bar{v}$ is $|\bar{v}| = \sqrt{1^2 + (-2)^2 + 2^2} = \sqrt{1 + 4 + 4} = \sqrt{9} = 3$.The unit vector in the direction of $\bar{v}$ is $\hat{v} = \frac{\bar{v}}{|\bar{v}|} = \frac{1}{3}(\hat{i} - 2\hat{j} + 2\hat{k})$.The required vector of magnitude $6$ is $6 	imes \hat{v} = 6 	imes \frac{1}{3}(\hat{i} - 2\hat{j} + 2\hat{k}) = 2(\hat{i} - 2\hat{j} + 2\hat{k}) = 2\hat{i} - 4\hat{j} + 4\hat{k}$.

If $\bar{a} = \hat{i} + \hat{j} + \hat{k}$,$\bar{b} = 4\hat{i} - 2\hat{j} + 3\hat{k}$,and $\bar{c} = \hat{i} - 2\hat{j} + \hat{k}$,then the vector of magnitude $6$ units,which is parallel to the vector $2\bar{a} - \bar{b} + 3\bar{c}$,is:

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