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11. three dimension geometry — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMaths11. three dimension geometry1 Mark
MCQ
If lines $\frac{{x - 1}}{3} = \frac{{y - 2}}{{ - 1}} = \frac{{z - \lambda }}{2}$ and $\frac{{x + 1}}{{ - 2}} = \frac{y}{{3\lambda }} = \frac{{2z - 7}}{1}$ are coplanar then sum of value $(s)$ of $\lambda $ is
  • ✓
    $\frac{{182}}{{36}}$
  • B
    $\frac{{162}}{{36}}$
  • C
    $\frac{{72}}{{36}}$
  • D
    $\frac{{182}}{2}$
✓

Answer

Correct option: A.
$\frac{{182}}{{36}}$
a
$\left|\begin{array}{ccc}{2} & {2} & {\lambda-\frac{7}{2}} \\ {3} & {-1} & {2} \\ {-2} & {3 \lambda} & {\frac{1}{2}}\end{array}\right|=0$

$\Rightarrow 2\left(-\frac{1}{2}-6 \lambda\right)-2\left(\frac{3}{2}+4\right)+\left(\lambda-\frac{7}{2}\right)(9 \lambda-2)=0$

$\Rightarrow 18 \lambda^{2}-91 \lambda-16=0$

$\Rightarrow \lambda_{1}+\lambda_{2}=\frac{91}{18}=\frac{182}{36}$

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