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10. vector algebra — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMaths10. vector algebra1 Mark
MCQ
The number of distinct real values of $\lambda$, for which the vectors $-\lambda^2 \hat{i}+\hat{j}+\hat{k}, \hat{i}-\lambda^2 \hat{j}+\hat{k}$ and $\hat{i}+\hat{j}-\lambda^2 \hat{k}$ are coplanar, is
  • A
    zero
  • B
    one
  • ✓
    two
  • D
    three
✓

Answer

Correct option: C.
two
c
$\left|\begin{array}{ccc}-\lambda^2 & 1 & 1 \\ 1 & -\lambda^2 & 1 \\ 1 & 1 & -\lambda^2\end{array}\right|$ $=0 \Rightarrow \lambda^6-3 \lambda^2-2=0$

$\Rightarrow\left(1+\lambda^2\right)^2\left(\lambda^2-2\right)=0 \Rightarrow \lambda= \pm \sqrt{2}$.

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