For given vectors,vec{a}=2 hat{i}-hat{j}+2 ha | vedclass

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(A) Given vectors are $\vec{a} = 2\hat{i} - \hat{j} + 2\hat{k}$ and $\vec{b} = -\hat{i} + \hat{j} - \hat{k}$.First,calculate the sum $\vec{a} + \vec{b

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$\frac{1}{\sqrt{2}}\hat{i} + \frac{1}{\sqrt{2}}\hat{k}$

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(A) Given vectors are $\vec{a} = 2\hat{i} - \hat{j} + 2\hat{k}$ and $\vec{b} = -\hat{i} + \hat{j} - \hat{k}$.First,calculate the sum $\vec{a} + \vec{b}$:$\vec{a} + \vec{b} = (2 - 1)\hat{i} + (-1 + 1)\hat{j} + (2 - 1)\hat{k} = \hat{i} + 0\hat{j} + \hat{k} = \hat{i} + \hat{k}$.Next,find the magnitude of the resultant vector $\vec{a} + \vec{b}$:$|\vec{a} + \vec{b}| = \sqrt{1^2 + 0^2 + 1^2} = \sqrt{1 + 1} = \sqrt{2}$.The unit vector in the direction of $\vec{a} + \vec{b}$ is given by $\frac{\vec{a} + \vec{b}}{|\vec{a} + \vec{b}|}$:$\frac{\hat{i} + \hat{k}}{\sqrt{2}} = \frac{1}{\sqrt{2}}\hat{i} + \frac{1}{\sqrt{2}}\hat{k}$.

For given vectors,$\vec{a}=2 \hat{i}-\hat{j}+2 \hat{k}$ and $\vec{b}=-\hat{i}+\hat{j}-\hat{k},$ find the unit vector in the direction of the vector $\vec{a}+\vec{b}.$

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