A) 10
B) 5
C) 2
D) 1
Correct Answer: C
Solution :
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 \[\lambda =2\,=|\vec{a}|=|\vec{b}|\]
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