A) \[\vec{a}=-\vec{b}\]
B) \[\vec{a}\ne \vec{b}\]
C) \[|\vec{a}|=|\vec{b}|\]
D) \[\vec{a}=\vec{b}\]
Correct Answer: C
Solution :
\[(\vec{a}+\vec{b}).(\vec{a}-\vec{b})=0\] \[\Rightarrow \]\[\vec{a}.\vec{a}-\vec{a}.\vec{b}+\vec{b}.\vec{a}-\vec{b}.\vec{b}=0\] \[\Rightarrow \] \[|\vec{a}{{|}^{2}}-|\vec{b}{{|}^{2}}=0\] \[\Rightarrow \] \[|\vec{a}{{|}^{2}}=|\vec{b}{{|}^{2}}\] \[\Rightarrow \] \[|\vec{a}|=|\vec{b}|\]
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