question_answer

If p Cos\[\theta \] - q Sin\[\theta \] = \[\sqrt{{{\mathbf{p}}^{\mathbf{2}}}\mathbf{+}{{\mathbf{q}}^{\mathbf{2}}}\mathbf{-}{{\mathbf{r}}^{\mathbf{2}}}}\] then the value of \[p\,Sin\theta +q\,Cos\theta \] is equal to

A)  \[\sqrt{{{p}^{2}}+{{q}^{2}}+{{r}^{2}}}\]                                                

B)  \[\sqrt{{{p}^{2}}-{{q}^{2}}+{{r}^{2}}}\]

C)  \[\sqrt{{{p}^{2}}+{{q}^{2}}}\]     

D)  r

E) None of these