A) parallel
B) perpendicular
C) collinear
D) coplanar
Correct Answer: B
Solution :
\[[\overrightarrow{a}+\overrightarrow{b}]=[\overrightarrow{a}-\overrightarrow{b}]\] On squaring both sides, \[{{[\overrightarrow{a}+\overrightarrow{b}]}^{2}}={{[\overrightarrow{a}-\overrightarrow{b}]}^{2}}\] \[\Rightarrow \] \[\overrightarrow{{{a}^{2}}}+\overrightarrow{{{b}^{2}}}+2\overrightarrow{a}.\overrightarrow{b}=\overrightarrow{{{a}^{2}}}+\overrightarrow{{{b}^{2}}}-2\overrightarrow{a}.\overrightarrow{b}\] \[\Rightarrow \] \[4\overrightarrow{a}.\overrightarrow{b}=0\] \[\Rightarrow \] \[\overrightarrow{a}.\overrightarrow{b}=0\] Hence,\[\overrightarrow{a}\]and \[\overrightarrow{b}\]are perpendicular.
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