question_answer

Given that \[\vec{A}+\vec{B}=\vec{R}\]and\[{{\text{A}}^{\text{2}}}+{{\text{B}}^{\text{2}}}={{\text{R}}^{\text{2}}}\], find the angle between \[\vec{A}\]and\[\vec{B}\].

Answer:

                \[\vec{A}=(\text{3}\text{1})\text{\hat{i} }+\left( \text{2}-\text{ 2} \right)\text{\hat{j} }+\left[ \text{2}-\left( -\text{1} \right) \right]\text{\hat{k}}=\text{2\hat{i}}+0\text{\hat{j}}+\text{3\hat{k}}=\text{2\hat{i}}+\text{3\hat{k}}\]and\[\text{A }=\sqrt{{{2}^{2}}+{{3}^{2}}}=\sqrt{13}\].