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NDA 2013
Exam
NDA
Year
2013
Subject
Mathematics
Chapter
Vector Algebra

NDA 2013 · Mathematics · Vector Algebra

The position vectors of the points A and B are respectively 3 i -5...

The position vectors of the points AA and BB are respectively 3i^−5j^+2k^3 \hat{i}-5 \hat{j}+2 \hat{k} and i^+j^−k^\hat{i}+\hat{j}-\hat{k}. What is the length of ABA B ?

Options

  1. A11
  2. B9
  3. C7
  4. D6

Correct answer

C. 7

Step-by-step solution

AB→=(3−1)i^+(−5−1)j^+(2−(−1))k^=2i^−6j^+3k^∣AB→∣=(2)2+(−6)2+(3)2=4+36+9=49=7 units. \begin{aligned} \overrightarrow{\mathrm{AB}} & =(3-1) \hat{i}+(-5-1) \hat{j}+(2-(-1)) \hat{k} \\ & =2 \hat{i}-6 \hat{j}+3 \hat{k} \\ |\overrightarrow{\mathrm{AB}}| & =\sqrt{(2)^2+(-6)^2+(3)^2} \\ & =\sqrt{4+36+9}=\sqrt{49}=7 \text{ units. }\end{aligned}
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