Question

# If ( |hat{a}+hat{b}|=|hat{a}-hat{b}|, ) then find the angle between ( vec{a} ) and ( vec{b} )

Solution

( quad|hat{a}+hat{b}|=|vec{a}-hat{b}| )

( |hat{a}+hat{b}|^{2}=|vec{a}-vec{b}|^{2} )

( Rightarrow(a+b) cdot(hat{a}+hat{b})=(hat{a}-hat{b}) cdot(hat{a}-hat{b}) )

( Rightarrow|hat{a}|^{2}+left(left.hat{b}right|^{2}+2 hat{a} cdot hat{b}=|hat{a}|^{2}+|hat{b}|^{2}-2 hat{a} cdot hat{b}^{n}right. )

( Rightarrow quad 4 hat{a} cdot hat{b}=0 )

( Rightarrow hat{a} cdot hat{b}=0 )

( Rightarrow|hat{a}||hat{b}| cdot cos theta=0 )

( Rightarrow theta=pi{} / 2 )

Angle between (hat{a}) & (hat{b}) = (pi{} / 2 )