Vectors 3 Question 5
5. The number of distinct real values of $\lambda$, for which the
vectors $-\lambda^{2} \hat{\mathbf{i}}+\hat{\mathbf{j}}+\hat{\mathbf{k}}, \hat{\mathbf{i}}-\lambda^{2} \hat{\mathbf{j}}+\hat{\mathbf{k}}$ and $\hat{\mathbf{i}}+\hat{\mathbf{j}}-\lambda^{2} \hat{\mathbf{k}}$ are coplanar, is
(2007, 3M)
(a) 0
(b) 1
(c) 2
(d) 3
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Answer:
Correct Answer: 5. (c)
Solution:
- Since, given vectors are coplanar
$$ \begin{aligned} & \therefore \\ & \Rightarrow \quad \lambda^{6}-3 \lambda^{2}-2=0 \Rightarrow\left(1+\lambda^{2}\right)^{2}\left(\lambda^{2}-2\right)=0 \Rightarrow \lambda= \pm \sqrt{2} \end{aligned} $$
