# Tagged Questions

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### Euclidean space and vector field

Can someone explain me what a Euclidean space is? and more detailed what a vector field is? Or a continuous vector field
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### Find a parametrization of the intersection curve between surfaces

Find a parametrization of the intersection curve between the surfaces $−3x^2+2z=10$ and $4x^2+10y^2=5$. You should parametrize such that $y=k\sin(t)$ for some constant k. The answer should be in ...
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### When does this parametric curve cross itself?

Find the points where the curve given parametrically by$$\mathbf{r}(t)=\left(2+\cos\frac{3}{2}t\right)\left(\begin{matrix}\cos t\\\sin t\end{matrix}\right)$$crosses itself. So, I understand that ...
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### Finding the orthogonal family of curves to a given family of curves. I am missing some.

Given the family of curves: $F(x,y,x_0)=0$ where $F(x,y,x_0) = (x-x_0)^2 + y^2 - R^2\ ,\ x_0 \in \mathbb{R}$ find the orthogonal family. This is my attempt: I first get the differential equation ...
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### Prove using an example that there is no plane on R3 that contains every group of 4 points

Well, this is a homewrok question (which I know I should not be asking, but I cannot find an answer to this anywhere): The exercise is as follows: i) Find the equation of the plane of R3 that ...
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### Parameterized curve describing trajectory of thrown object

We describe the trajectory of a thrown object (neglecting friction and similiar effects) with the curve $$k(t) = \left(v_0\cos(\beta)t,\,v_0\sin(\beta)t-\frac{g}{2}t^2\right)$$ with ...
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### Find the area of the region determined by two curves

Find the area of the region $R$ given by two curves. So the region $R$ describes the area that is common between the two curves: \begin{align*} \text{Function 1: } r&= 2\sin(\theta)\\ ...
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### Is $r=2\cos(\theta)$ a one-petal polar function?

I'm currently learning about polar functions and their graphs in precalculus, and one of the questions on my homework is to identify the shape of the function $r=2\cos(\theta)$. We were taught that ...
Vector equation $r(t)=2\cos(t)\mathbf i + 3\sin(t)\mathbf j\ \ (0 \le t \le 2\pi)$ represents ellipse. I need to find curvature of this ellipse on endpoints of x and y axis that are given with ...