CUET · MATHS · PYQ PAPER 2023
The vectors \(\lambda \hat{i}+\hat{j}+2 \hat{k}, \hat{i}+\lambda \hat{j}-\hat{k}\) and \(2 \hat{i}-\hat{j}+\lambda \hat{k}\) are coplanar if :
- A \(\lambda=-2, \lambda=1 \pm \sqrt{3}\)
- B \(\lambda=0, \lambda=-1 \pm \sqrt{3}\)
- C \(\lambda=1, \lambda= \pm 1+\sqrt{5}\)
- D \(\lambda=-1, \lambda=1, \lambda=\sqrt{3}\)
Answer & Solution
Correct Answer
(A) \(\lambda=-2, \lambda=1 \pm \sqrt{3}\)
Step-by-step Solution
Detailed explanation
\( \begin{vmatrix} \lambda & 1 & 2 \\ 1 & \lambda & -1 \\ 2 & -1 & \lambda \end{vmatrix} = 0 \) \( \lambda(\lambda^2 - 1) - 1(\lambda + 2) + 2(-1 - 2\lambda) = 0 \) \( \lambda^3 - 6\lambda - 4 = 0 \) \( (\lambda+2)(\lambda^2-2\lambda-2) = 0 \)…
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