Classify the following measure as a scalar or a vector: $40$ $watt$.

If the position vectors of $P$ and $Q$ are $(i + 3j - 7k)$ and $(5i - 2j + 4k)$,then $|\overrightarrow{PQ}|$ is

If vectors $\overrightarrow{a}_{1} = x \hat{i} - \hat{j} + \hat{k}$ and $\overrightarrow{a}_{2} = \hat{i} + y \hat{j} + z \hat{k}$ are collinear,then a possible unit vector parallel to the vector $x \hat{i} + y \hat{j} + z \hat{k}$ is ...... .

If $\hat{i}+2 \hat{j}+3 \hat{k}$ and $3 \hat{i}+2 \hat{j}+\hat{k}$ are sides of a parallelogram,then a unit vector parallel to one of the diagonals of the parallelogram is

Three vectors $\vec{P}, \vec{Q}$ and $\vec{R}$ are shown in the figure. Let $S$ be any point on the vector $\vec{R}$. The distance between the point $P$ and $S$ is $b|\vec{R}|$. The general relation among vectors $\vec{P}, \vec{Q}$ and $\vec{S}$ is

In a $\triangle ABC$ (shown in the figure below),state whether the following are true or false:
$(i)$ $\vec{AB} + \vec{BC} + \vec{CA} = \vec{0}$
(ii) $\vec{AB} + \vec{BC} - \vec{AC} = \vec{0}$
(iii) $\vec{AB} - \vec{CB} + \vec{CA} = \vec{0}$
(iv) $\vec{AB} + \vec{BC} - \vec{CA} = \vec{0}$