The unit vector parallel to the resultant vec | vedclass

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Question

(A) Let the given vectors be $\vec{a} = 2i + 4j - 5k$ and $\vec{b} = i + 2j + 3k$. The resultant vector $\vec{R}$ is the sum of $\vec{a}$ and $\vec{b}

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

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(A) Let the given vectors be $\vec{a} = 2i + 4j - 5k$ and $\vec{b} = i + 2j + 3k$. The resultant vector $\vec{R}$ is the sum of $\vec{a}$ and $\vec{b}$: $\vec{R} = \vec{a} + \vec{b} = (2+1)i + (4+2)j + (-5+3)k = 3i + 6j - 2k$. The magnitude of the resultant vector is $|\vec{R}| = \sqrt{3^2 + 6^2 + (-2)^2} = \sqrt{9 + 36 + 4} = \sqrt{49} = 7$. The unit vector $\hat{R}$ parallel to $\vec{R}$ is given by $\hat{R} = \frac{\vec{R}}{|\vec{R}|} = \frac{3i + 6j - 2k}{7} = \frac{1}{7}(3i + 6j - 2k)$.

The unit vector parallel to the resultant vector of $2i + 4j - 5k$ and $i + 2j + 3k$ is

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