The position vectors of the points $A, B, C$ are $(2\hat{i}+\hat{j}-\hat{k}), (3\hat{i}-2\hat{j}+\hat{k})$ and $(\hat{i}+4\hat{j}-3\hat{k})$ respectively. These points

If the vectors represented by the sides $AB$ and $BC$ of the regular hexagon $ABCDEF$ are $a$ and $b$ respectively,then the vector represented by $\overrightarrow{AE}$ will be

In a right-angled triangle,if the position vector of the vertex having the right angle is $\vec{A} = -3\hat{i} + 5\hat{j} + 2\hat{k}$ and the position vector of the midpoint of its hypotenuse is $\vec{M} = 6\hat{i} + 2\hat{j} + 5\hat{k}$,then the position vector of its centroid is

If $D, E, F$ are the midpoints of the sides $BC, CA, AB$ of a triangle $ABC$ respectively,find the position vector of the centroid of $\Delta DEF$,given that the position vectors of $A, B, C$ are $i + j, j + k, k + i$ respectively.

In a quadrilateral $ABCD$,$M$ and $N$ are the mid-points of the sides $AB$ and $CD$ respectively. If $\vec{AD} + \vec{BC} = t \vec{MN}$,then $t =$

Classify the following measure as a scalar or a vector:
$40^{o}$