question_answer

What is the property of two vectors \[\vec{A}\]and \[\vec{B}\], If \[|\vec{A}+\vec{B}|=|\vec{A}-\vec{B}|\].

Answer:

                Let\[\vec{A}=(\overrightarrow{OC})\];\[\vec{B}=(\overrightarrow{OD})\]and \[\vec{R}=(\overrightarrow{OF})\]; \[\angle \text{DOF}=\theta \] Fig. 2(c).54. Resolving \[\vec{B}\] into two rectangular components, we have: \[\text{B cos}\theta \]along OF and \[\text{B sin}\theta \]along OE. Here resultant vector is along OF. \[\text{R}=\text{B cos}\theta \]. As per question, \[\text{R}=\text{B}/\text{2}=\text{Bcos}\theta \] or\[\text{cos}\theta =1/2\] or\[\theta =\text{6}0{}^\circ \] Hence, angle between \[\vec{A}\]and \[\vec{B}\]\[\angle \text{COD }=\text{9}0{}^\circ +\text{6}0{}^\circ =\text{15}0{}^\circ \]