A) \[[\mathbf{a}\,\,\mathbf{b}\,\,\mathbf{c}]=0\]
B) \[[\mathbf{a}\,\,\mathbf{b}\,\,\mathbf{c}]\ne 0\]
C) \[[\mathbf{a}\,\,\mathbf{b}\,\,\mathbf{c}]=1\]
D) None of these
Correct Answer: A
Solution :
Since \[\mathbf{x}\]is a non-zero vector, the given conditions will be satisfied, if either (i) at least one of the vectors \[\mathbf{a},\,\,\mathbf{b},\,\,\mathbf{c}\] is zero or (ii) \[\mathbf{x}\] is perpendicular to all the vectors \[\mathbf{a},\,\,\mathbf{b},\,\,\mathbf{c}.\] In case (ii), \[\mathbf{a},\,\,\mathbf{b},\,\,\mathbf{c}\] are coplanar and so \[[\mathbf{a}\,\,\mathbf{b}\,\,\mathbf{c}]=0.\]
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