JEE Main & Advanced
Mathematics
Vector Algebra
Question Bank
Critical Thinking
question_answer
If \[\alpha \,(\mathbf{a}\times \mathbf{b})+\beta \,(\mathbf{b}\times \mathbf{c})+\gamma \,(\mathbf{c}\times \mathbf{a})=\mathbf{0}\] and at least one of the numbers \[\alpha ,\,\,\beta \] and \[\gamma \] is non-zero, then the vectors a, b and c are
A)Perpendicular
B)Parallel
C)Coplanar
D)None of these
Correct Answer:
C
Solution :
Let \[\alpha \ne 0,\] then \[\alpha (\mathbf{a}\times \mathbf{b})\,.\,\mathbf{c}+\beta (\mathbf{b}\times \mathbf{c})\,.\,\mathbf{c}+\gamma (\mathbf{c}\times \mathbf{a})\,.\,\mathbf{c}=0\,\]