A) a rectangle
B) a square
C) a rhombus
D) none of these
Correct Answer: A
Solution :
Let \[\overrightarrow{OA}=\overrightarrow{a}\] and \[\overrightarrow{OB}=\overrightarrow{b}\]. Complete the parallelogram OACB. |
\[\overrightarrow{a}+\overrightarrow{b}=\overrightarrow{OA}+\overrightarrow{OB}=\overrightarrow{OC}\] \[\Rightarrow \left| \overrightarrow{a}+\overrightarrow{b} \right|=OC\] |
Again \[\overrightarrow{a}-\overrightarrow{b}=\overrightarrow{OA}-\overrightarrow{OB}=\overrightarrow{BA}\] \[\Rightarrow \left| \overrightarrow{a}-\overrightarrow{b} \right|=BA\] |
Given \[\left| \overrightarrow{a}+\overrightarrow{b} \right|=\left| \overrightarrow{a}-\overrightarrow{b} \right|\Rightarrow \operatorname{OC}=BA\] |
\[\therefore \]Diagonals of the parallelogram OACB are equal. |
\[\therefore \]\[\overrightarrow{\operatorname{a}}\]and \[\overrightarrow{\operatorname{b}}\]are adjacent sides of a rectangle. |
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