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(A) The resultant vector $\vec{R} = \vec{P} + \vec{Q} = (2\hat{i} + 7\hat{j} - 10\hat{k}) + (\hat{i} + 2\hat{j} + 3\hat{k})$.$\vec{R} = (2+1)\hat{i} +

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$-2\hat{i} - 9\hat{j} + 7\hat{k}$

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(A) The resultant vector $\vec{R} = \vec{P} + \vec{Q} = (2\hat{i} + 7\hat{j} - 10\hat{k}) + (\hat{i} + 2\hat{j} + 3\hat{k})$.$\vec{R} = (2+1)\hat{i} + (7+2)\hat{j} + (-10+3)\hat{k} = 3\hat{i} + 9\hat{j} - 7\hat{k}$.Let the required vector be $\vec{S}$. We are given that $\vec{R} + \vec{S} = \hat{i}$ (the unit vector along the $X$-axis).Therefore,$\vec{S} = \hat{i} - \vec{R} = \hat{i} - (3\hat{i} + 9\hat{j} - 7\hat{k})$.$\vec{S} = (1-3)\hat{i} - 9\hat{j} + 7\hat{k} = -2\hat{i} - 9\hat{j} + 7\hat{k}$.

Which vector must be added to the resultant vector $\vec{P} = 2\hat{i} + 7\hat{j} - 10\hat{k}$ and $\vec{Q} = \hat{i} + 2\hat{j} + 3\hat{k}$ to obtain a unit vector along the $X$-axis?

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