${\vec A }$, ${\vec B }$ and ${\vec C }$ are three non-collinear, non co-planar vectors. What can you say about directin of $\vec A \, \times \,\left( {\vec B \, \times \vec {\,C} } \right)$ ?
The direction of $(\vec{B} \times \vec{C})$ will be perpendicular to the plane containing $\vec{B}$ and $\vec{C}$. $\vec{A} \times(\vec{B} \times \vec{C})$ will lie in the plane of $\vec{B}$ and $\vec{C}$ and is perpendicular to $\vec{A}$.
Show that the magnitude of a vector is equal to the square root of the scalar product of the vector with itself.
Find the angle between two vectors with the help of scalar product.
The angle between the vectors $(\hat i + \hat j)$ and $(\hat j + \hat k)$ is ....... $^o$
The angle made by the vector $\left( {\hat i\,\, + \;\,\hat j} \right)$ with $x-$ axis and $y$ axis is