A) \[\sqrt{{{A}^{2}}+{{B}^{2}}}\]
B) \[A+B\]
C) \[\sqrt{{{A}^{2}}+{{B}^{2}}+\frac{AB}{\sqrt{2}}}\]
D) \[\sqrt{{{A}^{2}}+{{B}^{2}}+\sqrt{2}AB}\]
Correct Answer: D
Solution :
\[AB\,\,\,\cos \theta =AB\,\sin \theta \] \[\Rightarrow \] \[\tan \theta =1\] \[\Rightarrow \] \[\theta ={{45}^{o}}\] \[\therefore \] \[|\overrightarrow{c}|=\sqrt{{{A}^{2}}+{{B}^{2}}+2AB\,\,\cos {{45}^{o}}}\] \[=\sqrt{{{A}^{2}}+{{B}^{2}}+\sqrt{2}AB}\]
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