If $|A|=2, |B|=5$ and $|A \times B|=8$. If the angle between $A$ and $B$ is acute,then $A \cdot B$ is

Vector $A$ is pointing eastwards and vector $B$ is pointing northwards. Match the following two columns:

Column $I$	Column $II$
$(A) (A+B)$	$(p)$ North-east
$(B) (A-B)$	$(q)$ Vertically upwards
$(C) (A \times B)$	$(r)$ Vertically downwards
$(D) (A \times B) \times (A \times B)$	$(s)$ None

Consider three vectors $A = \hat{i} + \hat{j} - 2\hat{k}$,$B = \hat{i} - \hat{j} + \hat{k}$,and $C = 2\hat{i} - 3\hat{j} + 4\hat{k}$. $A$ vector $X$ of the form $X = \alpha A + \beta B$ (where $\alpha$ and $\beta$ are scalars) is perpendicular to $C$. The ratio of $\alpha$ to $\beta$ is: (in $: 1$)

If $\vec{A}$ and $\vec{B}$ are vectors,which of the following statements is incorrect?

If diagonals of a parallelogram are $(5\hat i - 4\hat j + 3\hat k)$ and $(3\hat i + 2\hat j - \hat k)$,then its area is

Define the scalar product of two vectors.