Question

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 1

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

\(cos⁡θ=\frac{|\vec{a}|.|\vec{b}|}{\vec{a}.\vec{b}}\)

∴\(cos⁡θ=\frac{2.\sqrt{3}}{4}=\frac{\sqrt{3}}{2}\)

∴\(θ=cos^{-1}⁡\frac{\sqrt{3}}{2}=\frac{π}{6}\).