question_answer

The magnitude of vectors\[\vec{A}\], \[\vec{B}\] and \[\vec{C}\] are 12, 5 and 13 units respectively and\[\vec{A}+\,\vec{B}=\vec{C}\], find the angle Between\[\vec{A}\]and\[\vec{B}\].                

Answer:

Since\[{{\left( \text{12} \right)}^{\text{2}}}+{{\left( \text{5} \right)}^{\text{2}}}={{\left( \text{13} \right)}^{\text{2}}}\], so\[{{\text{A}}^{\text{2}}}+{{B}^{\text{2}}}={{\text{C}}^{\text{2}}}\]. It means the angle between \[\vec{A}\]and \[\vec{B}\]is\[\text{9}0{}^\circ \].