If $2 \vec{a} \cdot \vec{b}=|\vec{a}| \cdot |\vec{b}|$ then the angle between $\vec{a}$ and $\vec{b}$ is

If $2 \vec{a} \cdot \vec{b}=|\vec{a}| \cdot |\vec{b}|$ then the angle between $\vec{a}$ and $\vec{b}$ is
  1. \( 30^{\circ} \)
  2. \( 0^{\circ} \)
  3. \( 90^{\circ} \)
  4. \( 60^{\circ} \)

Solution

Given that, \( 2 \vec{a} \cdot \vec{b}=|\vec{a}| \cdot|\vec{b}| \)
As we know, \( \vec{a} \cdot \vec{b}=|\vec{a}||\vec{b}| \cos \theta \)
So, \( 2|\vec{a}||\vec{b}| \cos \theta=|\vec{a}||\vec{b}| \)
\( \Rightarrow 2 \cos \theta=1 \)
\( \Rightarrow \cos \theta=\frac{1}{2} \Rightarrow \theta=60^{\circ} \)

Asked in: TEST SERIES MHT-CET Full Test 6

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