• # question_answer If $\vec{a},\vec{b}$ are any two perpendicular vectors of equal magnitude and $\left| 3\vec{a}+4\vec{b} \right|+\left| 4\vec{a}-3\vec{b} \right|=20$, then $\left| {\vec{a}} \right|$ equals A)  10                                B)  5 C)  2                                 D)  1

Let $|\vec{a}|=|\vec{b}|=\lambda (>0)\,$ and $\vec{a}.\vec{b}=0$ (Given) Now $|3\vec{a}+4\vec{b}{{|}^{2}}\,=9{{\lambda }^{2}}\,+16{{\lambda }^{2}}\,=25{{\lambda }^{2}}$   ?(1) And $|4\vec{a}-3\vec{b}{{|}^{2}}\,=16{{\lambda }^{2}}\,+9{{\lambda }^{2}}\,=25{{\lambda }^{2}}$     ?(2) $\therefore$ From (1) and (2), we get $|3\vec{a}+4\vec{b}|\,+|4\vec{a}-3\vec{b}|=5\lambda +5\lambda =20$ (Given) Hence $\lambda =2\,=|\vec{a}|=|\vec{b}|$