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NDA 2023
Exam
NDA
Year
2023
Subject
Mathematics
Chapter
Vector Algebra

NDA 2023 · Mathematics · Vector Algebra

What is the length of projection of the vector i +2 j +3 k on the...

What is the length of projection of the vector i^+2j^+3k^\hat{i}+2 \hat{j}+3 \hat{k} on the vector 2i^+3j^−2k^2 \hat{i}+3 \hat{j}-2 \hat{k} ?

Options

  1. A117\frac{1}{\sqrt{17}}
  2. B217\frac{2}{\sqrt{17}}
  3. C317\frac{3}{\sqrt{17}}
  4. D214\frac{2}{\sqrt{14}}

Correct answer

B. 217\frac{2}{\sqrt{17}}

Step-by-step solution

Length of projection of the vector i^+2j^+3k^\hat{i}+2 \hat{j}+3 \hat{k} on the vector 2i^+3j^−2k^2 \hat{i}+3 \hat{j}-2 \hat{k} is (i^+2j^+3k^)⋅(2i^+3j^−2k^)∣2i^+3j^−2k^∣=2+6−64+9+4=217\frac{(\hat{i}+2 \hat{j}+3 \hat{k}) \cdot(2 \hat{i}+3 \hat{j}-2 \hat{k})}{|2 \hat{i}+3 \hat{j}-2 \hat{k}|}=\frac{2+6-6}{\sqrt{4+9+4}}=\frac{2}{\sqrt{17}}
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