If \left | \vec{a} \right |=2, \: |\vec{b}|=7 \: and \: \vec{a}\times \vec{b}=3\hat{i}+2\hat{j}+6\hat{k}, find the angle between \vec{a} \: \: and\: \: \vec{b}.

 

 

 

 

 
 
 
 
 

Answers (1)

\left | \vec{a} \right |=2, \: |\vec{b}|=7 \: and \: \left [\vec{a}\times \vec{b} \right ]=3\hat{i}+2\hat{j}+6\hat{k}

\therefore Angle \: between \:\vec{a}\: \: \: and\: \: \vec{b}\: is\: given\: by

\sin \theta =\frac{\left | \vec{a}\times \vec{b} \right |}{\left | \vec{a} \right |\left | \vec{b} \right |}\: \: \: \: -(i)

then, \left | \vec{a}\times \vec{b}\right| = \sqrt{(3)^2+(2)^2+(6)^2}

                         \Rightarrow \sqrt{49}=7

\therefore \sin \theta =\frac{7}{2 \times 7}=\frac{1}{2}

 \Rightarrow \sin \theta =\sin \frac{\pi }{6}\: \: \: \theta =\frac{\pi }{6}

 

 

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