Question

Find the angle between the two vectors \(\vec{a}\) and \(\vec{b}\) with magnitude \(\sqrt{3}\) and \(\sqrt{2}\) respectively and \(\vec{a.} \,\vec{b}=3\sqrt{2}\).

(a) \(cos^{-1}⁡\frac{1}{\sqrt{3}}\)

(b) \(cos^{-1}⁡\sqrt{3}\)

(c) \(cos^{-1}⁡\frac{3}{\sqrt{2}}\)

(d) \(cos^{-1}⁡\frac{2}{\sqrt{3}}\)

I got this question during an internship interview.

Asked question is from Product of Two Vectors-1 in chapter Vector Algebra of Mathematics – Class 12

Answer 1

Correct answer is (a) \(cos^{-1}⁡\frac{1}{\sqrt{3}}\)

Explanation: Given that, \(|\vec{a}|=\sqrt{3} \,and \,|\vec{b}|=\sqrt{2}\)

Also, \(\vec{a.} \vec{b}=3\sqrt{2}\)

The angle between two vectors is given by

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

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

∴\(θ=cos^{-1}⁡\frac{1}{\sqrt{3}}\).