If vec{r}_1 = 2hat{i} + 4hat{j} - 5hat{k} and | vedclass

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(C) The resultant vector $\vec{R}$ is given by $\vec{R} = \vec{r}_1 + \vec{r}_2$. Substituting the given vectors: $\vec{R} = (2\hat{i} + 4\hat{j} - 5\

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

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(C) The resultant vector $\vec{R}$ is given by $\vec{R} = \vec{r}_1 + \vec{r}_2$. Substituting the given vectors: $\vec{R} = (2\hat{i} + 4\hat{j} - 5\hat{k}) + (\hat{i} + 2\hat{j} + 3\hat{k}) = 3\hat{i} + 6\hat{j} - 2\hat{k}$. 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 $\hat{u}$ parallel to $\vec{R}$ is given by $\hat{u} = \frac{\vec{R}}{|\vec{R}|} = \frac{3\hat{i} + 6\hat{j} - 2\hat{k}}{7}$.

If $\vec{r}_1 = 2\hat{i} + 4\hat{j} - 5\hat{k}$ and $\vec{r}_2 = \hat{i} + 2\hat{j} + 3\hat{k}$,find the unit vector parallel to the resultant vector of $\vec{r}_1$ and $\vec{r}_2$.

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