Find the angle between the vectors \vec{a}=\hat{i}-\hat{j}+2\hat{k} \,and \,\vec{b}=3\hat{i}+2\hat{j}+4\hat{k}.

Category: QuestionsFind the angle between the vectors \vec{a}=\hat{i}-\hat{j}+2\hat{k} \,and \,\vec{b}=3\hat{i}+2\hat{j}+4\hat{k}.
Editor">Editor Staff asked 11 months ago

Find the angle between the vectors \vec{a}=\hat{i}-\hat{j}+2\hat{k} \,and \,\vec{b}=3\hat{i}+2\hat{j}+4\hat{k}.
(a) cos^{-1}⁡\sqrt{\frac{58}{3}}
(b) cos^{-1}⁡\frac{\sqrt{58}}{3}
(c) cos^{-1}\frac{⁡58}{3\sqrt{3}}
(d) cos^{-1}⁡\frac{\sqrt{58}}{3\sqrt{3}}
This question was addressed to me in a national level competition.
This interesting question is from Product of Two Vectors-1 in division Vector Algebra of Mathematics – Class 12
NCERT Solutions for Subject Clas 12 Math Select the correct answer from above options 
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1 Answers
Editor">Editor Staff answered 11 months ago

The correct option is (d) cos^{-1}⁡\frac{\sqrt{58}}{3\sqrt{3}}
To explain: The angle between the two vectors is given by