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(B) The resultant vector $\vec{R}$ is given by the sum of vectors $\vec{A}$ and $\vec{B}$:$\vec{R} = \vec{A} + \vec{B} = (4\hat{i} - 3\hat{j}) + (8\ha

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$\frac{12\hat{i} + 5\hat{j}}{13}$

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(B) The resultant vector $\vec{R}$ is given by the sum of vectors $\vec{A}$ and $\vec{B}$:$\vec{R} = \vec{A} + \vec{B} = (4\hat{i} - 3\hat{j}) + (8\hat{i} + 8\hat{j})$$\vec{R} = (4 + 8)\hat{i} + (-3 + 8)\hat{j} = 12\hat{i} + 5\hat{j}$The magnitude of the resultant vector is:$|\vec{R}| = \sqrt{12^2 + 5^2} = \sqrt{144 + 25} = \sqrt{169} = 13$The unit vector $\hat{R}$ parallel to the resultant is given by:$\hat{R} = \frac{\vec{R}}{|\vec{R}|} = \frac{12\hat{i} + 5\hat{j}}{13}$

The unit vector parallel to the resultant of vectors $\vec{A} = 4\hat{i} - 3\hat{j}$ and $\vec{B} = 8\hat{i} + 8\hat{j}$ is:

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