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STD 12 - 10. vector algebra — Mathematics STD 12 Science — Question

CBSE BoardEnglish MediumSTD 12 ScienceMathematicsSTD 12 - 10. vector algebra1 Mark
MCQ
If the four points, whose position vectors are $3 \hat{ i }-4 \hat{ j }+2 \hat{ k }, \hat{ i }+2 \hat{ j }-\hat{ k },-2 \hat{ i }-\hat{ j }+3 \hat{ k } \quad$ and $5 \hat{ i }-2 \alpha \hat{ j }+4 \hat{ k }$ are coplanar, then $\alpha$ is equal to
  • ✓
    $\frac{73}{17}$
  • B
    $-\frac{107}{17}$
  • C
    $-\frac{73}{17}$
  • D
    $\frac{107}{17}$
✓

Answer

Correct option: A.
$\frac{73}{17}$
a
Let $A:(3,-4,2)$ $C :(-2,-1,3)$ B : $(1,2,-1) \quad$ D : $(5,-2 \alpha, 4)$

$A, B, C, D$ are coplanar points, then

$\begin{array}{l}\Rightarrow\left|\begin{array}{ccc}1-3 & 2+4 & -1-2 \\ -2-3 & -1+4 & 3-2 \\ 5-3 & -2 \alpha+4 & 4-2\end{array}\right|=0\end{array}$

$\Rightarrow \alpha=\frac{73}{17}$

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