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GUJCET · Maths · Vector Algebra

સદિશો \(\vec{a}\) અને \(\vec{b}\) માટે, \(|\vec{a}|=3,|\vec{b}|=\frac{\sqrt{2}}{3}\) છે. તથા \(\vec{a} \times \vec{b}\) એકમ સદિશ છે, તો \(\vec{a}\) અને \(\vec{b}\) વચ્ચેના ખૂણાનું _________છે.

  1. A \(\frac{\pi}{4}\)
  2. B \(\frac{\pi}{2}\)
  3. C \(\frac{\pi}{6}\)
  4. D \(\frac{\pi}{3}\)
Verified Solution

Answer & Solution

Correct Answer

(A) \(\frac{\pi}{4}\)

Step-by-step Solution

Detailed explanation

\(|\vec{a} \times \vec{b}| = |\vec{a}| |\vec{b}| \sin \theta\) \(1 = (3) \left(\frac{\sqrt{2}}{3}\right) \sin \theta\)
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