If-A-p-x-p-y-p-z-is-a-position-vector-in-standard-position-vector-r-r-x-r-y-r-z-is-the-radius-of-a-3-dimensional-circle-with-focal-point-at-A-Solve-for-the-vector-equation-r-such-t

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Question Number 2092 by Filup last updated on 02/Nov/15

$$\mathrm{If}\mathit{A}=⟨p_x,p_y,p_z⟩\mathrm{is}\mathrm{a}\mathrm{position}\mathrm{vector}$$$$\mathrm{in}\mathrm{standard}\mathrm{position},\mathrm{vector}\mathit{r}=⟨r_x,r_y,r_z⟩$$$$\mathrm{is}\mathrm{the}\mathrm{radius}\mathrm{of}\mathrm{a}3\mathrm{dimensional}\mathrm{circle}$$$$\mathrm{with}\mathrm{focal}\mathrm{point}\mathrm{at}\mathit{A},\mathrm{Solve}\mathrm{for}\mathrm{the}$$$$\mathrm{vector}\mathrm{equation}\mathit{r}\left(\theta \right)\mathrm{such}\mathrm{that}\mathrm{it}\mathrm{is}\mathrm{the}$$$$\mathrm{equation}\mathrm{of}\mathrm{a}3\mathrm{dimensional}\mathrm{circle}$$

Commented by Filup last updated on 02/Nov/15

$$\mathrm{Solve}\mathrm{such}\mathrm{that}\mathrm{it}\mathrm{is}\mathrm{in}\mathrm{form}:$$$$\mathit{r}\left(\theta \right)=⟨x\left(\theta \right),y\left(\theta \right),z\left(\theta \right)⟩$$

Commented by prakash jain last updated on 03/Nov/15

$$\mathrm{You}\mathrm{have}\mathrm{a}\mathrm{point}\mathrm{and}\mathrm{radius}\mathrm{vector}\mathrm{in}3\mathrm{D}.$$$$\mathrm{There}\mathrm{will}\mathrm{be}\mathrm{many}\mathrm{circles}\mathrm{possible}.$$

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