Let $u, v$ and $w$ be non-coplanar vectors. Then the points corresponding to which of the following vectors are collinear?

If the vector $a = 2 \hat{i} + 3 \hat{j} + 6 \hat{k}$ and $b$ are collinear and $|b| = 21$, then $b$ is equal to:

If three points $A$,$B$,and $C$ have position vectors $(1, x, 3)$,$(3, 4, 7)$,and $(y, -2, -5)$ respectively and if they are collinear,then $(x, y)$ is

Vector $\vec{x}$ is a vector in the direction of $(2, -2, 1)$ and has a magnitude of $6$ units. Vector $\vec{y}$ is a vector in the direction of $(1, 1, -1)$ and has a magnitude of $\sqrt{3}$ units. Then,$|\vec{x} + 2\vec{y}| = $ . . . . . . .

If $a = 3i - 2j + k$,$b = 2i - 4j - 3k$ and $c = -i + 2j + 2k$,then $a + b + c$ is

Suppose that $\bar{p}, \bar{q}$ and $\bar{r}$ are three non-coplanar vectors in $\mathbb{R}^3$. Let the components of a vector $\bar{s}$ along $\bar{p}, \bar{q}$ and $\bar{r}$ be $4, 3$ and $5$ respectively. If the components of this vector $\bar{s}$ along $(-\bar{p}+\bar{q}+\bar{r}), (\bar{p}-\bar{q}+\bar{r})$ and $(-\bar{p}-\bar{q}+\bar{r})$ are $x, y$ and $z$ respectively,then the value of $2x+y+z$ is