Match Column $-I$ with Column $-II$.

Column $-I$	Column $-II$
$(1)$ Angular momentum	$(a)$ Scalar
$(2)$ Potential energy	$(b)$ Vector
	$(c)$ Unit vector

If a vector $\overrightarrow{P}$ makes angles $\alpha, \beta,$ and $\gamma$ with the $X, Y,$ and $Z$ axes respectively,then $\sin^2 \alpha + \sin^2 \beta + \sin^2 \gamma = $

In a regular octagon $ABCDEFGH$ with center $O$,what is the sum of $\overrightarrow{ AB }+\overrightarrow{ AC }+\overrightarrow{ AD }+\overrightarrow{ AE }+\overrightarrow{ AF }+\overrightarrow{ AG }+\overrightarrow{ AH }$ if $\overrightarrow{ AO }=2 \hat{ i }+3 \hat{ j }-4 \hat{ k }$?

If two vectors $2\hat{i} + 3\hat{j} - \hat{k}$ and $-4\hat{i} - 6\hat{j} + \lambda\hat{k}$ are parallel to each other,then the value of $\lambda$ is:

$A$ unit vector is represented as $(0.8 \hat{i} + b \hat{j} + 0.4 \hat{k})$. Hence,the value of $b$ must be:

A body cools according to Newton's law of cooling from $100^\circ C$ to $60^\circ C$ in $20$ minutes. The temperature of the surroundings being $20^\circ C$, then the total time required for the body to cool down to $30^\circ C$ is