If $\vec{a}=4 \hat{i}+13 \hat{j}-18 \hat{k}$,$\vec{b}=\hat{i}-2 \hat{j}+3 \hat{k}$,and $\vec{c}=2 \hat{i}+3 \hat{j}-4 \hat{k}$ are three vectors such that $\vec{a}=x \vec{b}+y \vec{c}$,then $x+y=$

The position vectors of two points $A$ and $B$ are $\hat{i} + \hat{j} - \hat{k}$ and $2\hat{i} - \hat{j} + \hat{k}$ respectively. Then $|\overrightarrow{AB}| = $

If the position vector of one end of the line segment $AB$ is $2\hat{i} + 3\hat{j} - \hat{k}$ and the position vector of its midpoint is $3\,(\hat{i} + \hat{j} + \hat{k}),$ then the position vector of the other end is

If $A, B, C$ are the vertices of a triangle whose position vectors are $a, b, c$ and $G$ is the centroid of the $\Delta ABC$,then $\overrightarrow{GA} + \overrightarrow{GB} + \overrightarrow{GC}$ is

If $a, b, c$ are the position vectors of the vertices $A, B, C$ of the triangle $ABC,$ then the centroid of $\Delta ABC$ is

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