The vectors $\mathbf{a}$ lies in the plane of vectors $\mathbf{b}$ and $\mathbf{c}$, then

The vectors $\mathbf{a}$ lies in the plane of vectors $\mathbf{b}$ and $\mathbf{c}$, then
  1. $[\mathbf{a} \mathbf{b} \mathbf{c}]$
  2. $[\mathbf{a} \mathbf{b} \mathbf{c}]=\mathbf{b} \mathbf{c}$
  3. $[\mathbf{a} \mathbf{b} \mathbf{c}]=0$
  4. $[\mathbf{a} \mathbf{b} \mathbf{c}]=-1$

Solution

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} $

Asked in: AP EAMCET 2021 (25 Aug Shift 1)

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