Find the values of $x, y$ and $z$ so that the vectors $\vec{a} = x \hat{i} + 2 \hat{j} + z \hat{k}$ and $\vec{b} = 2 \hat{i} + y \hat{j} + \hat{k}$ are equal.

Statement $(A):$ In $\Delta ABC$,$\overline{AB} + \overline{BC} + \overline{CA} = 0$.
Reason $(R):$ If $\overline{AB} = \vec{a}$ and $\overline{BC} = \vec{b}$,then $\overline{AC} = \vec{a} + \vec{b}$ (Triangle Law of Addition).

If $PQRST$ is a pentagon,then the resultant of forces $\overline{PQ}, \overline{PT}, \overline{QR}, \overline{SR}, \overline{TS}$ and $\overline{PS}$ is

$A$ point $C$ with position vector $\frac{3 \bar{a}+4 \bar{b}-5 \bar{c}}{3}$ (where $\bar{a}, \bar{b}$ and $\bar{c}$ are non-coplanar vectors) divides the line segment joining $A$ and $B$ in the ratio $2:1$. If the position vector of $A$ is $\bar{a}-2 \bar{b}+3 \bar{c}$,then find the position vector of $B$.

$(a \cdot i)i + (a \cdot j)j + (a \cdot k)k = $

Classify the following measure as a scalar or a vector:
$10 \text{ Newton}$