A) \[{{a}^{2}}+{{b}^{2}}\]
B) \[a+b\]
C) \[\sqrt{{{a}^{2}}-{{b}^{2}}}\]
D) \[\sqrt{{{a}^{2}}+{{b}^{2}}}\]
Correct Answer: D
Solution :
(d): Distance =\[\sqrt{{{(a\,\,cos\,\,\theta +b\,\,\sin \,\,\theta -0)}^{2}}+{{(0-a\,\,sin\,\,\theta +b\,\,\cos \,\,\theta )}^{2}}}\] \[=\sqrt{{{a}^{2}}\,{{\cos }^{2}}\theta +{{b}^{2}}{{\sin }^{2}}\theta +2ab\,\cos \,\theta \,\sin \,\theta +{{b}^{2}}\,{{\cos }^{2}}\theta +{{a}^{2}}{{\sin }^{2}}\theta -2ab\,\sin \theta \,\cos \,\theta }\] \[=\sqrt{{{a}^{2}}+{{b}^{2}}}\]
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