A) [a b c]
B) 2 [a b c]
C) 3 [a b c]
D) 0
Correct Answer: D
Solution :
\[[\mathbf{a}+\mathbf{b}\,\,\mathbf{b}+\mathbf{c}\,\,\mathbf{c}+\mathbf{a}]\]\[=[\mathbf{a}\,\mathbf{b}\,\mathbf{c}]+[\mathbf{a}\,\mathbf{b}\,\mathbf{a}]+[\mathbf{a}\,\mathbf{c}\,\mathbf{c}]\] \[+[\mathbf{a}\,\mathbf{c}\,\mathbf{a}]+[\mathbf{b}\,\mathbf{b}\,\mathbf{c}]+[\mathbf{b}\,\mathbf{b}\,\mathbf{a}]+[\mathbf{b}\,\mathbf{c}\,\mathbf{c}]+[\mathbf{b}\,\mathbf{c}\,\mathbf{a}]\] \[=[\mathbf{a}\,\mathbf{b}\,\mathbf{c}]+[\mathbf{b}\,\mathbf{c}\,\mathbf{a}]=2[\mathbf{a}\,\mathbf{b}\,\mathbf{c}]=0\], (\[\because \]a,b,c are coplanar).
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