The vector that must be added to the vectors | vedclass

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(B) Let the required vector be $\vec{R}$.Given vectors are $\vec{A} = \hat{i} - 3\hat{j} + 2\hat{k}$ and $\vec{B} = 3\hat{i} + 6\hat{j} - 7\hat{k}$.Th

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$-4\hat{i} - 2\hat{j} + 5\hat{k}$

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(B) Let the required vector be $\vec{R}$.Given vectors are $\vec{A} = \hat{i} - 3\hat{j} + 2\hat{k}$ and $\vec{B} = 3\hat{i} + 6\hat{j} - 7\hat{k}$.The resultant vector is a unit vector along the $y$-axis,which is $\hat{j}$.According to the problem,$\vec{A} + \vec{B} + \vec{R} = \hat{j}$.First,calculate the sum of $\vec{A}$ and $\vec{B}$:$\vec{A} + \vec{B} = (1+3)\hat{i} + (-3+6)\hat{j} + (2-7)\hat{k} = 4\hat{i} + 3\hat{j} - 5\hat{k}$.Now,substitute this into the equation:$4\hat{i} + 3\hat{j} - 5\hat{k} + \vec{R} = \hat{j}$.$\vec{R} = \hat{j} - (4\hat{i} + 3\hat{j} - 5\hat{k})$.$\vec{R} = -4\hat{i} + (1-3)\hat{j} + 5\hat{k}$.$\vec{R} = -4\hat{i} - 2\hat{j} + 5\hat{k}$.

The vector that must be added to the vectors $\hat{i} - 3\hat{j} + 2\hat{k}$ and $3\hat{i} + 6\hat{j} - 7\hat{k}$ so that the resultant vector is a unit vector along the $y$-axis is

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