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NDA 2013
Exam
NDA
Year
2013
Subject
Mathematics
Chapter
Vector Algebra

NDA 2013 · Mathematics · Vector Algebra

For any vector α , what is ( α · i ) i +( α · j ) j +( α · k ) k...

For any vector α⃗\vec{\alpha}, what is (α⃗⋅i^)i^+(α⃗⋅j^)j^+(α⃗⋅k^)k^(\vec{\alpha} \cdot \hat{i}) \hat{i}+(\vec{\alpha} \cdot \hat{j}) \hat{j}+(\vec{\alpha} \cdot \hat{k}) \hat{k} equal to?

Options

  1. Aα⃗\vec{\alpha}
  2. B3α⃗3 \vec{\alpha}
  3. C−α⃗-\vec{\alpha}
  4. D0→\overrightarrow{0}

Correct answer

A. α⃗\vec{\alpha}

Step-by-step solution

α⃗=a1i^+a2j^+a3k^\vec{\alpha}=a_1 \hat{i}+a_2 \hat{j}+a_3 \hat{k} take dot with i^,j^andk^\hat{i}, \hat{j} and \hat{k} on both sides you get α⃗⋅i^=a1,a2=α⃗⋅j^,a3=α⃗⋅k^α⃗=(α⃗⋅i^)i^+(α⃗⋅j^)j^+(α⃗⋅k^)k^\begin{aligned} & \vec{\alpha} \cdot \hat{i}=a_1, \quad a_2=\vec{\alpha} \cdot \hat{j}, \quad a_3=\vec{\alpha} \cdot \hat{k} \\ & \vec{\alpha}=(\vec{\alpha} \cdot \hat{i}) \hat{i}+(\vec{\alpha} \cdot \hat{j}) \hat{j}+(\vec{\alpha} \cdot \hat{k}) \hat{k}\end{aligned}
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