Assertion (A): If | a × b |^2+| a · b |^2=256 and | b |=8, then | a |=2 Reason (R): sin^2 θ+ cos^2 θ=1 and | a × b |=| a || b | sin θ and a · b =| a…

Assertion (A): If $\displaystyle |\overrightarrow{\mathrm{a}} \times \overrightarrow{\mathrm{b}}|^{2}+|\overrightarrow{\mathrm{a}} \cdot \overrightarrow{\mathrm{b}}|^{2}=256$ and $\displaystyle |\overrightarrow{\mathrm{b}}|=8$, then \[|\overrightarrow{\mathrm{a}}|=2 \] Reason $\displaystyle (R): \quad \sin ^{2} \theta+\cos ^{2} \theta=1$ and \[|\overrightarrow{\mathrm{a}} \times \overrightarrow{\mathrm{b}}|=|\overrightarrow{\mathrm{a}}||\overrightarrow{\mathrm{b}}| \sin \theta \text { and } \overrightarrow{\mathrm{a}} \cdot \overrightarrow{\mathrm{~b}}=|\overrightarrow{\mathrm{a}}||\overrightarrow{\mathrm{b}}| \cos \theta \]