Let $\vec{a}$ and $\vec{b}$ be two vectors such that $|\vec{a}|=1,|\vec{b}|=4$ and $\vec{a} \cdot \vec{b}=2$. If $\vec{c}=(2 \vec{a} \times \vec{b})-3 \vec{b}$ and the angle between $\vec{b}$...

Let the line of the shortest distance between the lines $\mathrm{L}_1: \vec{r}=(\hat{\imath}+2 \hat{\jmath}+3 \hat{k})+\lambda(\hat{\imath}-\hat{\jmath}+\hat{k})$ and $\mathrm{L}_2: \overrightarrow{\mathrm{r}}= (4 \hat{\imath}+5 \hat{\jmath}+6 \hat{k})+\mu(\hat{\imath}+\hat{\jmath}-\hat{k})$ intersect $L_1$ and $L_2$...