Question

Under what condition will the direction of sum and difference of two vectors be same?

Answer 1

For $\overrightarrow{A}+\overrightarrow{B}=\overrightarrow{A}-\overrightarrow{B}$

$\Rightarrow \overrightarrow{A}=0,or\overrightarrow{B}=0,or\overrightarrow{A}and\overrightarrow{B}=0$

so, if the direction of sum and difference of two vectors be same either one of them or both of them are zero vector.