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Vectors — Maths STD 12 Science — Question

Maharashtra BoardEnglish MediumSTD 12 ScienceMathsVectors2 Marks
MCQ
If a vector $\bar{\alpha}$ lie in the plane $\bar{\beta}$ and $\bar{\gamma}$, then which is correct?
  • ✓
    $\left[\begin{array}{lll}\bar{\alpha} & \bar{\beta} & \bar{\gamma}\end{array}\right]=0$
  • B
    $\left[\begin{array}{lll}\bar{\alpha} & \bar{\beta} & \bar{\gamma}\end{array}\right]=1$
  • C
    $\left[\begin{array}{lll}\bar{\alpha} & \bar{\beta} & \bar{\gamma}\end{array}\right]=3$
  • D
    $\left[\begin{array}{lll}\bar{\beta} & \bar{\gamma} & \bar{\alpha}\end{array}\right]=1$
✓

Answer

Correct option: A.
$\left[\begin{array}{lll}\bar{\alpha} & \bar{\beta} & \bar{\gamma}\end{array}\right]=0$
(A) Vector $\bar{\alpha}$ lies in the plane of $\bar{\beta}$ and $\bar{\gamma}$
$\begin{array}{ll}\therefore & \bar{\alpha}, \bar{\beta}, \bar{\gamma} \text { are coplanar. } \\ & \Rightarrow[\bar{\alpha} \bar{\beta} \bar{\gamma}]=0\end{array}$

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