Vector Algebra Question 177
Question: 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
Options:
A) Perpendicular
B) Parallel
C) Coplanar
D) None of these
Show Answer
Answer:
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, $
$ \Rightarrow \alpha [\mathbf{a},\mathbf{b},\mathbf{c}]=0\Rightarrow [\mathbf{a},\mathbf{b},\mathbf{c}]=0 $ , $ { \because ,\alpha \ne 0 } $
Hence a, b, c are coplanar.
BETA
