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

Explain cross product of two vectors.

Show that the scalar product of two vectors obeys the law of distributive.

Three particles ${P}, {Q}$ and ${R}$ are moving along the vectors ${A}=\hat{{i}}+\hat{{j}}, {B}=\hat{{j}}+\hat{{k}}$ and ${C}=-\hat{{i}}+\hat{{j}}$ respectively. They strike on a point and start to move in different directions. Now particle $P$ is moving normal to the plane which contains vector $\vec{A}$ and $\vec{B} .$ Similarly particle $Q$ is moving normal to the plane which contains vector $\vec{A}$ and $\vec{C} .$ The angle between the direction of motion of $P$ and $Q$ is $\cos ^{-1}\left(\frac{1}{\sqrt{x}}\right)$. Then the value of $x$ is ...... .

What is the product of two vectors if they are parallel or antiparallel ? 

The resultant of $\vec{A} \times 0$ will be equal to