question_answer

If the magnitude of vectors \[\vec{A}\], \[\vec{B}\]and \[\vec{C}\]are 3, 4 and 5 units respectively, and if \[\vec{A}+\,\vec{B}=\vec{C}\], find the angle between \[\vec{A}\] and\[\vec{B}\].                

Answer:

Since\[{{\text{A}}^{\text{2}}}+{{\text{B}}^{\text{2}}}={{\text{C}}^{\text{2}}}\]; therefore angle between \[\vec{A}\]and \[\vec{B}\] is\[\text{9}0{}^\circ \]. Let \[\theta \]be the angle between \[\vec{A}\]and\[\vec{C}\], then\[\text{cos}\theta =\text{3}/\text{5}\]or \[\theta =\text{co}{{\text{s}}^{-\text{1}}}\left( \text{3}/\text{5} \right)\].