JEE Mains · Maths · STD 12 - 10. vector algebra
If the volume of parallelepiped formed by the vectors \(\hat i + \lambda \hat j + \hat k\), \(\hat j + \lambda \hat k\) and \(\lambda \hat i + \hat k\) is minimum, then \(\lambda \) is equal to
- A \(\sqrt 3 \)
- B \(\frac{1}{{\sqrt 3 }}\)
- C \(-\frac{1}{{\sqrt 3 }}\)
- D None of these
Answer & Solution
Correct Answer
(D) None of these
Step-by-step Solution
Detailed explanation
Volume of paralleopiped \( = \left\| {\begin{array}{*{20}{l}} 1&\lambda &1\\ 0&1&\lambda \\ \lambda &0&1 \end{array}} \right\|\) \(f(\lambda)=\left|\lambda^{3}-\lambda+1\right|\) Its graphs as follows where \(\lambda=-1.32\) For minimum value of volume of paralelopiped and…
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