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AP EAMCET · Maths · Vector Algebra

If the magnitudes of \(\bar{a}, \bar{b}\) and \(\bar{a}+\bar{b}\) are respectively 3,4 and 5, then the magnitude of \(\bar{a}-\bar{b}\) is

  1. A \(3\)
  2. B \(4\)
  3. C \(6\)
  4. D \(5\)
Verified Solution

Answer & Solution

Correct Answer

(D) \(5\)

Step-by-step Solution

Detailed explanation

\( |\bar{a}+\bar{b}|^2 = |\bar{a}|^2 + |\bar{b}|^2 + 2\bar{a}\cdot\bar{b} \) \( 5^2 = 3^2 + 4^2 + 2\bar{a}\cdot\bar{b} \) \( 25 = 9 + 16 + 2\bar{a}\cdot\bar{b} \) \( 25 = 25 + 2\bar{a}\cdot\bar{b} \Rightarrow 2\bar{a}\cdot\bar{b} = 0 \)…