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  4. The value of λ ∈ R such that (x, y, z) ≠(0,0,0) and ( hati+ hatj+3 hatk) x+(3 hati-3 hatj+ hatk) y+(-4 hati+5 hatj) z=λ(x hati+y hatj+z hatk) can be

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Q. The value of $\lambda \in R$ such that $(x, y, z) \neq(0,0,0)$ and $(\hat{i}+\hat{j}+3 \hat{k}) x+(3 \hat{i}-3 \hat{j}+\hat{k}) y+(-4 \hat{i}+5 \hat{j}) z=\lambda(x \hat{i}+y \hat{j}+z \hat{k})$ can be

Vector Algebra

Solution:

$\begin{vmatrix}1-\lambda & 3 & -4 \\ 1 & -3-\lambda & 5 \\ 3 & 1 & -\lambda\end{vmatrix}=0$ gives $\lambda(\lambda+1)^2=0$