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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 m if the vectors 2 i - j + k , i +2 j -3 k and...

What is the value of mm if the vectors 2i^−j^+k^2 \hat{i}-\hat{j}+\hat{k}, i^+2j^−3k^\hat{i}+2 \hat{j}-3 \hat{k} and 3i^+mj^+5k^3 \hat{i}+m \hat{j}+5 \hat{k} are coplanar?

Options

  1. A-2
  2. B2
  3. C-4
  4. D4

Correct answer

C. -4

Step-by-step solution

∣2−1112−33m5∣=02(10+3m)+1(5+9)+1(m−6)=020+6m+14+m−6=07m+28=07=−4.\begin{aligned} & \left|\begin{array}{ccc}2 & -1 & 1 \\ 1 & 2 & -3 \\ 3 & m & 5\end{array}\right|=0 \\ & \begin{array}{l}2(10+3 m)+1(5+9)+1(m-6)=0 \\ 20+6 m+14+m-6=0 \\ 7 m+28=0\end{array} \\ & \begin{array}{l}7=-4.\end{array}\end{aligned}
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