AP EAMCET · Maths · Vector Algebra
The set of real values of \(\lambda\) for which the vectors \(\lambda \hat{i}-3 \hat{j}+5 \hat{k}\) and \(2 \lambda \hat{i}-\lambda \hat{j}+\hat{k}\) are perpendicular to each other is
- A \(\{0,1\}\)
- B \(\{-2\}\)
- C \(\{2,-1\}\)
- D \(\phi\)
Answer & Solution
Correct Answer
(D) \(\phi\)
Step-by-step Solution
Detailed explanation
\[ \begin{aligned} & (\lambda \hat{i}-3 \hat{j}+5 \hat{k}) \cdot(2 \lambda \hat{i}-\lambda \hat{j}+\hat{k})=0 \\ & \Rightarrow \quad 2 \lambda^2+3 \lambda+5=0 \\ & \end{aligned} \] as \(D=9-40 < 0\), no real values of \(\lambda\) satisty the equation.
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