The number of distinct real values of λ , for which the vectors − λ 2 i ^ + j ^ + k ^ , i ^ − λ 2 j ^ + k ^ and i ^ + j ^ − λ 2 k ^ are coplanar, is

− λ 2 1 1 1 − λ 2 1 1 1 − λ 2 = 0 ⇒ λ 6 − 3 λ 2 − 2 = 0 ⇒ ( 1 + λ 2 ) 2 ( λ 2 − 2 ) = 0 ⇒ λ = ± 2

Mathematics - Vector Question with Solution | TestHub

MathematicsVectorSTPEasy2 minPYQ_2007

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The number of distinct real values of $λ$ , for which the vectors $- λ^{2} \hat{i} + \hat{j} + \hat{k}$ , $\hat{i} - λ^{2} \hat{j} + \hat{k}$ and $\hat{i} + \hat{j} - λ^{2} \hat{k}$ are coplanar, is

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Answer:

Solution:

$- λ^{2} 11 1 - λ^{2} 1 11 - λ^{2} = 0 \Rightarrow λ^{6} - 3 λ^{2} - 2 = 0 \Rightarrow (1 + λ^{2})^{2} (λ^{2} - 2) = 0 \Rightarrow λ = \pm 2$

Stream:JEE_ADVSubject:MathematicsTopic:VectorSubtopic:STP

⏱ 2mℹ️ Source: PYQ_2007

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