A) 47
B) 25
C) 50
D) ? 25
Correct Answer: D
Solution :
\[\because \] \[\mathbf{a}+\mathbf{b}+\mathbf{c}=0\] Squaring both sides, we get \[|\mathbf{a}{{|}^{2}}+|\mathbf{b}{{|}^{2}}+|\mathbf{c}{{|}^{2}}+\,2(\mathbf{a}\,.\,\mathbf{b}+\mathbf{b}\,.\,\mathbf{c}\,+\mathbf{c}\,.\,\mathbf{a})=0\] \[\Rightarrow 2(\mathbf{a}\,.\,\mathbf{b}+\mathbf{b}\,.\,\mathbf{c}+\mathbf{c}\,.\,\mathbf{a})=-\,(9+16+25)\] \[\Rightarrow \,\mathbf{a}\,.\,\mathbf{b}+\mathbf{b}\,.\,\mathbf{c}+\mathbf{c}\,.\,\mathbf{a}=-25.\]
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