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Question

Mathematics Question on Vector Algebra

The number of distinct real values of λ\lambda, for which the vectors −λ2i^+j^+k^,i^−λ2j^+k^-\lambda^2\widehat{i}+\widehat{j}+\widehat{k}, \widehat{i}-\lambda^2\widehat{j}+\widehat{k} and i^+j^−λ2k^\widehat{i}+\widehat{j}-\lambda^2\widehat{k} are coplanar, is

A

0

B

1

C

2

D

3

Answer

2

Explanation

Solution

Since, given vectors are coplanar
\therefore\hspace25mm\begin{array}|-\lambda^2&1&1\\\1&-\lambda^2&1\\\1&0&-\lambda^2\\\\\end{array}=0
⇒λ6−3λ2−2=0⇒(1+λ2)2(λ2−2)=0⇒λ=±2\Rightarrow \lambda^6-3\lambda^2-2=0 \Rightarrow (1+\lambda^2)^2(\lambda^2-2)=0\Rightarrow \lambda=\pm \sqrt{2}