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NDA 2011
Exam
NDA
Year
2011
Subject
Mathematics
Chapter
Vector Algebra

NDA 2011 · Mathematics · Vector Algebra

What is the projection of the vector i -2 j + k on the vector 4 i...

What is the projection of the vector i^−2j^+k^\hat{i}-2 \hat{j}+\hat{k} on the vector 4i^−4j^+7k^4 \hat{i}-4 \hat{j}+7 \hat{k} ?

Options

  1. A52\frac{\sqrt{5}}{2}
  2. B199\frac{19}{9}
  3. C54\frac{\sqrt{5}}{4}
  4. D113\frac{11}{3}

Correct answer

B. 199\frac{19}{9}

Step-by-step solution

Projection of the vector i^−2j^+k^\hat{i}-2 \hat{j}+\hat{k} on the vector 4i^−4j^+7k^=(i^−2j^+k^)⋅(4i^−4j^+7k^)∣4i^−4j^+7k^∣=4+8+716+16+49=1981=199.\begin{aligned} 4 \hat{i}-4 \hat{j}+7 \hat{k} & =\frac{(\hat{i}-2 \hat{j}+\hat{k}) \cdot(4 \hat{i}-4 \hat{j}+7 \hat{k})}{|4 \hat{i}-4 \hat{j}+7 \hat{k}|} \\ & =\frac{4+8+7}{\sqrt{16+16+49}}=\frac{19}{\sqrt{81}}=\frac{19}{9} . \end{aligned}
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