Feb 3, 2025 · Use the computed normal vector $ (n_1, n_2, n_3) $ to form the equation. Step 4: Expand and Simplify. Expand the equation to get it in standard Cartesian form: $$ Ax + By + Cz + D = 0 $$ Where $ A, B, C $ come from the normal vector and $ D $ is obtained from substituting $ (x_0, y_0, z_0) $. Details are left to you. I hope it helps.

Jun 22, 2012 · I am supposed to find a Cartesian equation by eliminating the parameters of ... This equation can be ...

I'm trying to find the cartesian equation of the curve which is defined parametrically by: $$ x = 2\sin\theta, y = \cos^2\theta $$ Both approaches I take result in the same answer: $$ y = 1 - \s...

May 5, 2016 · The solution to the original inhomogeneous equation is then the sum of any particular solution to that equation and this solution to the homogeneous equation. $(x,y,z)^T=(1,0,0)$ is an easy choice for a particular solution, resulting in the equation $$(x,y,z)^T=(1,0,0)^T+\lambda(3,1,0)^T+t(4,0,1)^T$$ for the plane.

Oct 2, 2011 · For purposes of plotting with a computer, the implicit equation isn't terribly convenient to handle, so I'll throw in a set of parametric Cartesian equations for free, based on the parametric equations of the Lamé curve:

Apr 5, 2017 · Find the vector equation of the line with Cartesian equation: $$5x + 1 = -10y - 4 = 2z$$ I know the vector equation of a line is $\textbf{r} × \textbf{v} = \textbf{a} × \textbf{v}$, where $\textbf{r}$ is the position vector of a point on the line, $\textbf{a}$ is a fixed point on the line, and $\textbf{v}$ is a direction vector for $\textit{L ...

Oct 29, 2015 · Finding the vector equation of a plane from cartesian. 0. Cartesian equations from given hyperplanes. 0.

May 28, 2013 · Stack Exchange Network. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.

A cartesian equation of a curve is simply finding the single equation of this curve in a standard form where xs and ys are the only variables. To find this equation, you need to solve the parametric equations simultaneously: If y = 4t, then divide both sides by 4 to find (1/4)y = t. This newly found value of t can be substituted into the ...

Sep 9, 2016 · Find a cartesian equation for the polar curve. Ask Question Asked 8 years, 7 months ago.