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:

  1. Since, given vectors are coplanar

$$ \begin{aligned} & \therefore \\ & \Rightarrow \quad \lambda^{6}-3 \lambda^{2}-2=0 \Rightarrow\left(1+\lambda^{2}\right)^{2}\left(\lambda^{2}-2\right)=0 \Rightarrow \lambda= \pm \sqrt{2} \end{aligned} $$



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