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NDA 2013
Exam
NDA
Year
2013
Subject
Mathematics
Chapter
Vector Algebra

NDA 2013 · Mathematics · Vector Algebra

If | a |= 2 ,| b |= 3 and | a + b |= 6 , then what is | a - b |...

If ∣a⃗∣=2,∣b⃗∣=3|\vec{a}|=\sqrt{2},|\vec{b}|=\sqrt{3} and ∣a⃗+b⃗∣=6|\vec{a}+\vec{b}|=\sqrt{6}, then what is ∣a⃗−b⃗∣|\vec{a}-\vec{b}| equal to?

Options

  1. A11
  2. B22
  3. C33
  4. D44

Correct answer

B. 22

Step-by-step solution

∣a⃗+b⃗∣2+∣a⃗−b⃗∣2=2(∣a⃗∣2+∣b⃗∣2)6+∣a⃗−b⃗∣2=2(2+3)∣a⃗−b⃗∣=2\begin{aligned} & |\vec{a}+\vec{b}|^2+|\vec{a}-\vec{b}|^2=2\left(|\vec{a}|^2+|\vec{b}|^2\right) \\ & 6+|\vec{a}-\vec{b}|^2=2(2+3) \\ & |\vec{a}-\vec{b}|=2\end{aligned}
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