A) a.b = 0
B) a × b = 0
C) a.a = b.b
D) None of these
Correct Answer: C
Solution :
\[\because \] \[\mathbf{a}\,.\,\mathbf{a}=|\mathbf{a}||\mathbf{a}|\,\,\cos \theta =|\mathbf{a}{{|}^{2}}\], \[(\because \theta ={{0}^{o}})\] and \[\mathbf{b}\,.\,\mathbf{b}=\,|\mathbf{b}||\mathbf{b}|\cos \theta =\,|\mathbf{b}{{|}^{2}}\], (Here\[\theta ={{0}^{o}}\]) Also, since \[\mathbf{a}\,\text{and}\,\mathbf{b}\] are sides of rhombus \ \[|\mathbf{a}|\,=\,|\mathbf{b}|\]. Hence \[\mathbf{a}\,.\,\mathbf{a}=\mathbf{b}\,.\,\mathbf{b}.\]
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