AP EAMCET · Maths · Vector Algebra
The vectors \(\mathbf{a}\) lies in the plane of vectors \(\mathbf{b}\) and \(\mathbf{c}\), then
- A \([\mathbf{a} \mathbf{b} \mathbf{c}]\)
- B \([\mathbf{a} \mathbf{b} \mathbf{c}]=\mathbf{b} \mathbf{c}\)
- C \([\mathbf{a} \mathbf{b} \mathbf{c}]=0\)
- D \([\mathbf{a} \mathbf{b} \mathbf{c}]=-1\)
Answer & Solution
Correct Answer
(C) \([\mathbf{a} \mathbf{b} \mathbf{c}]=0\)
Step-by-step Solution
Detailed explanation
Vector \(\mathbf{a}\) lie in the plane of vector \(\mathbf{b}\) and \(\mathbf{c}\). \(\therefore\) a,b, c are coplanar vectors. Hence, a \[ \begin{aligned} (\mathbf{b} \times \mathbf{c}) & =0 \\ {[\mathbf{a} \mathbf{b} \mathbf{c}] } & =0 \end{aligned} \]
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