The figure formed by the four points $i + j - k$,$2i + 3j$,$3i + 5j - 2k$,and $k - j$ is:

Let $\vec{u} = 2\hat{i} + 3\hat{j} + \hat{k}$,$\vec{v} = -3\hat{i} + 2\hat{j}$ and $\vec{w} = \hat{i} - \hat{j} + 4\hat{k}$. Then which of the following statements is true?

Let the points $A, B$ and $P$ be $(-2, 2, 4), (2, 6, 3)$ and $(1, 2, 1)$ respectively. The magnitude of the moment of the force represented by $\overrightarrow{AB}$ and acting at $A$ about $P$ is

Let $O$ be the origin and $PQR$ be an arbitrary triangle. If a point $S$ satisfies the condition $\overrightarrow{OP} \cdot \overrightarrow{OQ} + \overrightarrow{OR} \cdot \overrightarrow{OS} = \overrightarrow{OR} \cdot \overrightarrow{OP} + \overrightarrow{OQ} \cdot \overrightarrow{OS} = \overrightarrow{OQ} \cdot \overrightarrow{OR} + \overrightarrow{OP} \cdot \overrightarrow{OS}$,then the point $S$ is the:

If $|a \times b| = 4$ and $|a \cdot b| = 2$,then $|a|^2 |b|^2 = $

If $|a| = 3, |b| = 1, |c| = 4$ and $a + b + c = 0,$ then $a \cdot b + b \cdot c + c \cdot a = $