A) If \[\theta ={{45}^{o}},\] then \[\bigcirc -\vec{A}\times \vec{B}=-\vec{A}.\vec{B}\]
B) If \[\left| {\vec{A}} \right|=\left| {\vec{B}} \right|,\] then \[(\vec{A}+\vec{B})\] must be parallel to \[(\vec{A}-\vec{B})\]
C) If \[\vec{A}=\vec{O},\] then \[\left| \vec{A}+\vec{B} \right|=\left| \vec{A}-\vec{B} \right|\]
D) None of the above
Correct Answer: C
Solution :
If \[\vec{A}=\vec{O},\] the \[\left| \vec{A}+\vec{B} \right|=\left| \vec{A}-\vec{B} \right|\] \[\Rightarrow \] \[\left| \vec{O}+\vec{B} \right|=\left| \vec{O}-\vec{B} \right|\] \[\Rightarrow \] \[B=B\]
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