Consider the lines,

$${L_1}:{{x + 1} \over 3} = {{y + 2} \over 1} = {{z + 1} \over 2}$$

$${L_2}:{{x - 2} \over 1} = {{y - 2} \over 2} = {{z - 3} \over 3}$$

The shortest distance between $${L_1}$$ and $${L_2}$$ is :

Let $$\vec{a}, \vec{b}, \vec{c}$$ be unit vectors such that $$\vec{a}+\vec{b}+\vec{c}=\overrightarrow{0}$$. Which one of the following is correct?

The number of distinct real values of $$\lambda$$, for which the vectors $$ - {\lambda ^2}\widehat i + \widehat j + \widehat k,\widehat i - {\lambda ^2}\widehat j + \widehat k$$ and $$\widehat i + \widehat j - {\lambda ^2}\widehat k$$ are coplanar, is :