A) 5
B) 1
C) 6
D) 8
Correct Answer: C
Solution :
Let the position vectors of the points \[A,\,\,B,\,\,C\] are 0, \[\mathbf{a}+\mathbf{b},\,\,\mathbf{a}-\mathbf{b}\] and \[\theta =90{}^\circ .\] Area of triangle \[=\frac{1}{2}|\overrightarrow{AB}\times \overrightarrow{AC}|\] \[=\frac{1}{2}|(\mathbf{a}+\mathbf{b})\times (\mathbf{a}-\mathbf{b})|=\frac{1}{2}|2\mathbf{b}\times \mathbf{a}|\] \[=ba\sin \theta =3\times 2\sin 90{}^\circ =6.\]You need to login to perform this action.
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