Find the angle between the two vectors \(\vec{a} \,and \, \vec{b}\) with magnitude 2 and \(\sqrt{3}\) respectively and \(\vec{a.} \, \vec{b}\)=4.(a) \(\frac{π}{3}\)(b) \(\frac{π}{6}\)(c) \(cos^{-1}⁡\frac{\sqrt{2}}{3}\)(d) \(cos^{-1}⁡\frac{2}{\sqrt{3}}\)I have been asked this question in homework.I'm obligated to ask this question of Product of Two Vectors-1 topic in portion Vector Algebra of Mathematics – Class 12

Find the angle between the two vectors \(\vec{a} \,and \, \vec{b}\) wi

1.	Find the angle between the two vectors \(\vec{a} \,and \, \vec{b}\) with magnitude 2 and \(\sqrt{3}\) respectively and \(\vec{a.} \, \vec{b}\)=4.(a) \(\frac{π}{3}\)(b) \(\frac{π}{6}\)(c) \(cos^{-1}⁡\frac{\sqrt{2}}{3}\)(d) \(cos^{-1}⁡\frac{2}{\sqrt{3}}\)I have been asked this question in homework.I'm obligated to ask this question of Product of Two Vectors-1 topic in portion Vector Algebra of Mathematics – Class 12
Answer» CORRECT CHOICE is (b) \(\frac{π}{6}\) To explain: GIVEN that, \(\|\vec{a}\|=2 \,and \,\|\vec{b}\|=\sqrt{3}\) Also, \(\vec{a.} \,\vec{b}=4\) The ANGLE between two vectors is given by \(cos⁡θ=\frac{\|\vec{a}\|.\|\vec{b}\|}{\vec{a}.\vec{b}}\) ∴\(cos⁡θ=\frac{2.\sqrt{3}}{4}=\frac{\sqrt{3}}{2}\) ∴\(θ=cos^{-1}⁡\frac{\sqrt{3}}{2}=\frac{π}{6}\).

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