Two vectors $A$ and $B$ inclined at angle $\theta$ have a resultant $R$ which makes an angle $\phi$ with $A$. If the directions of $A$ and B are interchanged and resultant will have the same

$\vec{A}$ is a vector of magnitude $2.7$ units due east. What is the magnitude and direction of vector $4 \vec{A}$ ?

If $\left| {{{\vec v}_1} + {{\vec v}_2}} \right| = \left| {{{\vec v}_1} - {{\vec v}_2}} \right|$ and ${{{\vec v}_1}}$ and ${{{\vec v}_2}}$ are finite, then

Two vectors $\overrightarrow{ A }$ and $\overrightarrow{ B }$ have equal magnitudes. If magnitude of $\overrightarrow{ A }+\overrightarrow{ B }$ is equal to two times the magnitude of $\overrightarrow{ A }-\overrightarrow{ B }$, then the angle between $\overrightarrow{ A }$ and $\overrightarrow{ B }$ will be .......................

The vectors $\vec{A}$ and $\vec{B}$ are such that

$|\vec{A}+\vec{B}|=|\vec{A}-\vec{B}|$

The angle between the two vectors is

Explain commutative law for vector addition.