# Tagged Questions

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### (I only need some hints)Find the vector equation of a space curve that represents an ellipse with the given center that lies in the given plane

Full disclosure, this is for a Calculus III graded homework set--though we are allowed to use any resources available to complete it. I feel I have a good understanding of space curves, though my ...
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### surface that is created by the intersection of paraboloid and plane

Find the surface that is created by the intersection of the paraboloid $x^2+y^2-z=0$ and the plane $z=2$. $$x^2+y^2-z=0 \Rightarrow x^2+y^2=z$$ $$z=2$$ EDIT: I had to find the area of the surface ...
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### Find the equation of a plane [duplicate]

Find the equation of a plane that passes through point $P(1,5,1)$, and is perpendicular to the planes $2x+y-2z=2$ and $x+3z=4$ My only guess so far is that we can obtain the plane's normal vector ...
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### How do you find the acute angle between the lines: $x+2y=7$ and $5x-y=2$. [closed]

Find the acute angle between the lines: $x+2y=7$ and $5x-y=2$. Use vectors.
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### Clarification of the Jacobian

Well, that was cool if not tedious but I understand the Jacobian and its application to changing coordinate systems. $${J_{POLAR}= \rho}$$ $${J_{cyl}= \rho}$$ and $${J_{sphere}=\rho^2\sin\phi}$$ ...
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### Why is the Jacobian ${\rho}$

Just a little confused. When I find the volume of a cone (or a sphere) for that matter I multiply the partial derivatives by the Jacobian. ${\rho}$ for a cone. and ${\rho^2 \sin \phi}$ for a sphere. ...
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### Trying to understand Volume of a cone without the unit sphere

I have been working on the double integral proof for the volume of a cone. I found that I can use a unit-sphere Where the base of the cone is the equator and the height is the distance ${\rho}$ to ...
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### Can't find the derivation ${\rho^2\sin\phi}$

I have accepted that the equation of a sphere in spherical coordinates is ${\rho^2\sin\phi}$. The triple integral is just to nice. What I don't understand is what happened to ${\theta}$. How can you ...
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### Geometric Interpretation of Jacobi identity for cross product

Is there a geometric "reason" for the Jacobi identity for cross products? Some geometric equality of some area ...? All proofs I know work by some form of linear algebra (or use the interpretation as ...
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### boundary of the half-annulus

Question Let C be the boundary of the half-annulus a^2 < (x^2 + y^2) < b^2 and y>=0 in the x-y plane, traversed in the negative direction what is ∫ (5e^(-7x^2) - y^3) dx + x^3 +cosh^2(5y) dy ...
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### Find point on sphere with directional tangent vector

Say a sphere equation like this: $x^2+y^2+z^2=5$. I want to find a point on the sphere whose tangent vector is perpendicular to the vector $\begin{bmatrix} 2\\ 3\\ 4 \end{bmatrix}$. I go ...
If you dropped two rocks in a pond, the concentric circles emanating from the two spots would osculate $\infty$ times. The locus of osculating points would form a line. Now imagine that instead of ...