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NDA 2012
Exam
NDA
Year
2012
Subject
Mathematics
Chapter
Vector Algebra

NDA 2012 · Mathematics · Vector Algebra

What is the value of λ for which (λ i + j - k ) ×(3 i -2 j +4 k...

What is the value of λ\lambda for which (λi^+j^−k^)×(3i^−2j^+4k^)=(2i^−11j^−7k^)?(\lambda \hat{i}+\hat{j}-\hat{k}) \times(3 \hat{i}-2 \hat{j}+4 \hat{k})=(2 \hat{i}-11 \hat{j}-7 \hat{k}) ?

Options

  1. A2
  2. B-2
  3. C1
  4. D7

Correct answer

A. 2

Step-by-step solution

(\lambda \hat{i}+\hat{j}-k) \times(3 \hat{i}-2 \hat{j}+4 k)=2 \hat{i}-11 \hat{j}-7 \hat{k}\left|i^j^kλ1−13−24\begin{array}{ccc}\hat{i} & \hat{j} & k \\ \lambda & 1 & -1 \\ 3 & -2 & 4\end{array}\right|=2 \hat{i}-11 \hat{j}-7 \hat{k}\hat{i}(4-2)-\hat{j}(4 \lambda+3)+\hat{k}(-2 \lambda-3)=2 \hat{i}-11 \hat{j}-7 \hat{k} from above 4λ+3=11∴λ=24 \lambda+3=11\therefore \quad \lambda=2.
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