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

If $P$ divides the line segment joining the points $A$ and $B$ in the ratio $2:1$ and the position vectors of $A$ and $B$ are $\hat{i}-2\hat{j}$ and $-3\hat{i}+5\hat{j}$ respectively,then the position vector of $P$ is

Statement $(A):$ If $\vec{a}, \vec{b}, \vec{c}$ are unit vectors such that $\vec{a} + \vec{b} + \vec{c} = 0$,then $\vec{a} \cdot \vec{b} + \vec{b} \cdot \vec{c} + \vec{c} \cdot \vec{a} = -\frac{3}{2}$.
Reason $(R): (\vec{x} + \vec{y})^2 = |\vec{x}|^2 + |\vec{y}|^2 + 2(\vec{x} \cdot \vec{y})$.

Let $\vec{v}$ be a vector in the plane such that $|\vec{v} - \hat{i}| = |\vec{v} - 2\hat{j}| = |\vec{v} - \hat{j}|$. Then,$|\vec{v}|$ lies in the interval

If $PQ + QR = (2\lambda^2 - 5)RP$,then $\lambda$ is equal to

If a vector $a$ of magnitude $50$ is collinear with the vector $b = 6i - 8j - \frac{15}{2}k$, and makes an acute angle with the positive direction of the $z$-axis, then the vector $a$ is equal to: