question_answer 33)

                The angle between \[\vec{A}=\hat{i}+\hat{j}\] and \[\vec{B}\,=\,\hat{i}-\hat{j}\,\] is                 (a) \[{{45}^{o}}\]                                   (b) \[{{90}^{o}}\]                 (c) \[-\,{{45}^{o}}\]                       (d) \[{{180}^{o}}\]

Answer:

                (b) \[\cos \,\theta \,=\,\frac{\vec{A}\cdot \vec{B}}{|\vec{A}|\,|\vec{B}|}=\frac{(\hat{i}\,+\hat{j})\,(i-\hat{j})}{\sqrt{2}\,\times \,\sqrt{2}}\,=\frac{1-1}{2}=0\]                 \[\therefore \,\theta =\,\,{{90}^{o}}\]