If $i + 2j + 3k$ is parallel to the sum of the vectors $3i + \lambda j + 2k$ and $-2i + 3j + k$,then $\lambda = \dots$

If the position vectors of two points $A$ and $B$ are $\vec{a} - 3\vec{b}$ and $6\vec{b} - 2\vec{a}$ respectively,then the position vector of the point dividing $AB$ in the ratio $1 : 2$ is:

Let $ABC$ be a triangle whose circumcentre is at $P$. If the position vectors of $A, B, C$ and $P$ are $\vec{a}, \vec{b}, \vec{c}$ and $\frac{\vec{a} + \vec{b} + \vec{c}}{4}$ respectively,then the position vector of the orthocentre of this triangle is:

If $\vec{a} = -4\hat{i} + 2\hat{j} - 5\hat{k}$ and $\vec{b} = 12\hat{i} - 6\hat{j} + 15\hat{k}$,then the vectors $\vec{a}$ and $\vec{b}$ are $.......$

If $\vec{a}$ and $\vec{b}$ are non-collinear vectors,then the value of $\alpha$ for which the vectors $\vec{u} = (\alpha - 2)\vec{a} + \vec{b}$ and $\vec{v} = (2 + 3\alpha)\vec{a} - 3\vec{b}$ are collinear is:

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