If the line, $${{x - 3} \over 2} = {{y + 2} \over { - 1}} = {{z + 4} \over 3}\,$$ lies in the planes, $$lx+my-z=9,$$ then $${l^2} + {m^2}$$ is equal to :

Let $$\overrightarrow a ,\overrightarrow b $$ and $$\overrightarrow c $$ be three unit vectors such that $$\overrightarrow a \times \left( {\overrightarrow b \times \overrightarrow c } \right) = {{\sqrt 3 } \over 2}\left( {\overrightarrow b + \overrightarrow c } \right).$$ If $${\overrightarrow b }$$ is not parallel to $${\overrightarrow c },$$ then the angle between $${\overrightarrow a }$$ and $${\overrightarrow b }$$ is:

The distance of the point $$(1,-5,9)$$ from the plane $$x-y+z=5$$ measured along the line $$x=y=z$$ is :

The Boolean expression

$$\left( {p \wedge \sim q} \right) \vee q \vee \left( { \sim p \wedge q} \right)$$ is equivalent to :