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Question: Answered & Verified by Expert
The vectors $\mathbf{a}$ lies in the plane of vectors $\mathbf{b}$ and $\mathbf{c}$, then
MathematicsVector AlgebraAP EAMCETAP EAMCET 2021 (25 Aug Shift 1)
Options:
  • 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 $[\mathbf{a} \mathbf{b} \mathbf{c}]=-1$
Solution:
2820 Upvotes Verified Answer
The correct answer is: $[\mathbf{a} \mathbf{b} \mathbf{c}]=0$
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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