If $\vec{A}$ and $\vec{B}$ are two vectors satisfying the relation $\vec{A} . \vec{B}=[\vec{A} \times \vec{B}]$. Then the value of $[\vec{A}-\vec{B}]$. will be :
$\sqrt{A^{2}+B^{2}-\sqrt{2} A B}$
$\sqrt{A^{2}+B^{2}}$
$\sqrt{A^{2}+B^{2}+\sqrt{2} A B}$
$\sqrt{A^{2}+B^{2}+\sqrt{2} A B}$
Show that the magnitude of a vector is equal to the square root of the scalar product of the vector with itself.
Show that the scalar product of two vectors obeys the law of distributive.
$\vec{A}$ is a vector quantity such that $|\vec{A}|=$ nonzero constant. Which of the following expressions is true for $\vec{A}$ $?$
Show that the scalar product of two vectors obeys the law of commutative.