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If $\vec{F}=2\hat{i}+\hat{j}-\hat{k}$ and $\vec{r}=3\hat{i}+2\hat{j}-2\hat{k}$, then the scalar and vector products of $\vec{F}$ and $\vec{r}$ have the magnitudes respectively as:
Detailed Solution
$\vec{F}\cdot\vec{r}=2\times3+1\times2+(-1)(-2)=10$. $\vec{F}\times\vec{r}=\hat{i}(-2+2)-\hat{j}(-4+3)+\hat{k}(4-3)=\hat{j}+\hat{k}$, so $|\vec{F}\times\vec{r}|=\sqrt{2}$.