The unit vector parallel to the resultant of | vedclass

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(A) First,find the resultant vector $\vec R$ by adding vectors $\vec A$ and $\vec B$: $\vec R = \vec A + \vec B = (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) First,find the resultant vector $\vec R$ by adding vectors $\vec A$ and $\vec B$: $\vec R = \vec A + \vec B = (4\hat i + 3\hat j + 6\hat k) + (- \hat i + 3\hat j - 8\hat k)$ $\vec R = (4 - 1)\hat i + (3 + 3)\hat j + (6 - 8)\hat k = 3\hat i + 6\hat j - 2\hat k$ Next,calculate the magnitude of the resultant vector $|\vec R|$: $|\vec R| = \sqrt{3^2 + 6^2 + (-2)^2} = \sqrt{9 + 36 + 4} = \sqrt{49} = 7$ Finally,the unit vector $\hat R$ is given by $\hat R = \frac{\vec R}{|\vec R|}$: $\hat R = \frac{3\hat i + 6\hat j - 2\hat k}{7} = \frac{1}{7}(3\hat i + 6\hat j - 2\hat k)$

The unit vector parallel to the resultant of the vectors $\vec A = 4\hat i + 3\hat j + 6\hat k$ and $\vec B = - \hat i + 3\hat j - 8\hat k$ is

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