question_answer

Under what condition the magnitude of the sum of two vectors is equal to the magnitude of difference between them.                

Answer:

Given, \[|\vec{A}+\,\vec{B}|=|\vec{A}-\,\vec{B}|\]or\[{{\text{A}}^{\text{2}}}+{{\text{B}}^{\text{2}}}+\text{2AB}\,\text{cos}\theta ={{\text{A}}^{\text{2}}}+{{\text{B}}^{\text{2}}}\text{2ABcos}\theta \]. or \[\text{4 AB cos}\theta =0\]or\[\text{cos}\theta =0\]or\[\theta =\text{ 9}0{}^\circ \]. i.e. the two vectors are perpendicular to each other.