If the resultant vector of vectors vec{A} = 4 | vedclass

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(A) The resultant vector $\vec{R}$ is given by $\vec{R} = \vec{A} + \vec{B}$.Substituting the given vectors: $\vec{R} = (4\hat{i} + 3\hat{j} + 6\hat{k

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$\frac{1}{7}(3\hat{i} + 6\hat{j} - 2\hat{k})$

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(A) The resultant vector $\vec{R}$ is given by $\vec{R} = \vec{A} + \vec{B}$.Substituting the given vectors: $\vec{R} = (4\hat{i} + 3\hat{j} + 6\hat{k}) + (-\hat{i} + 3\hat{j} - 8\hat{k})$.Combining the components: $\vec{R} = (4-1)\hat{i} + (3+3)\hat{j} + (6-8)\hat{k} = 3\hat{i} + 6\hat{j} - 2\hat{k}$.The unit vector parallel to $\vec{R}$ is $\hat{R} = \frac{\vec{R}}{|\vec{R}|}$.First,calculate the magnitude $|\vec{R}| = \sqrt{3^2 + 6^2 + (-2)^2} = \sqrt{9 + 36 + 4} = \sqrt{49} = 7$.Therefore,the unit vector is $\hat{R} = \frac{3\hat{i} + 6\hat{j} - 2\hat{k}}{7} = \frac{1}{7}(3\hat{i} + 6\hat{j} - 2\hat{k})$.

If the resultant vector of vectors $\vec{A} = 4\hat{i} + 3\hat{j} + 6\hat{k}$ and $\vec{B} = -\hat{i} + 3\hat{j} - 8\hat{k}$ is parallel to a unit vector,then $\vec{R}$ is:

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