The position vectors of points P and Q are $\vec{p}$ and $\vec{q}$ respectively. The point $R$ divides line segment $P Q$ in the ratio $3: 1$ and S is the mid-point of line segment PR. The position vector of $S$ is

Assertion (A): The vectors

$$\begin{aligned} & \vec{a}=6 \hat{i}+2 \hat{j}-8 \hat{k} \\ & \vec{b}=10 \hat{i}-2 \hat{j}-6 \hat{k} \\ & \vec{c}=4 \hat{i}-4 \hat{j}+2 \hat{k} \end{aligned}$$

represent the sides of a right angled triangle.

Reason (R): Three non-zero vectors of which none of two are collinear forms a triangle if their resultant is zero vector or sum of any two vectors is equal to the third.

Two vector $$\vec{a}=a_1 \hat{i}+a_2 \hat{j}+a_3 \hat{k} \quad$$ and $$\vec{b}=b_1 \hat{i}+b_2 \hat{j}+b_3 \hat{k}$$ are collinear if:

The magnitude of the vector $$6 \hat{i}-2 \hat{j}+3 \hat{k}$$ is :