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NDA 2010
Exam
NDA
Year
2010
Subject
Mathematics
Chapter
Vector Algebra

NDA 2010 · Mathematics · Vector Algebra

What is the value of λ for which the vectors i - j + k , 2 i + j -...

What is the value of λ\lambda for which the vectors i^−j^+k^\hat{i}-\hat{j}+\hat{k}, 2i^+j^−k^,λi^−j^+λk^2 \hat{i}+\hat{j}-\hat{k}, \quad \lambda \hat{i}-\hat{j}+\lambda \hat{k}, are coplanar?

Options

  1. A1
  2. B2
  3. C3
  4. D4

Correct answer

A. 1

Step-by-step solution

x(i^−j^+k^)+y(2i^+j^−k^)=λi^−j^+λk^⇒(x+2y)i+(−x+y)j^+(x−y)k^=λi^−j^+λk^x+2y=λ3y=0,x=λy=0,λ=1\begin{aligned} & x(\hat{i}-\hat{j}+\hat{k})+y(2 \hat{i}+\hat{j}-\hat{k})=\lambda \hat{i}-\hat{j}+\lambda \hat{k} \\ & \Rightarrow(x+2 y) i+(-x+y) \hat{j}+(x-y) \hat{k}=\lambda \hat{i}-\hat{j}+\lambda \hat{k} \\ & x+2 y=\lambda \\ & 3 y=0, x=\lambda \\ & y=0, \lambda=1\end{aligned}
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