0
votes
2answers
326 views

Finding vector and parametric equations provided only one point.

Normally to answer these questions I have a point and one or two vectors. However, for this one I only have a point. How can I concoct these equations provided there is limited information? Find ...
1
vote
3answers
51 views

Is what I'm doing valid?

Find the POI of the following two planes: $$\pi_1: -3x + 3y + z + 6= 0$$ $$\pi_2: 3x - y + 2z - 2 = 0$$ I started by isolating "$z$". $$\pi_1: z = 3x - 3y - 6$$ $$\pi_2: z = \frac ...
0
votes
2answers
52 views

Ray-Lens Intersection

So imagine that I have a ray parameterized as $\vec{R} = \vec{O} + t\vec{D}$, where $\vec{O}$ = origin, $t$ = parameter and $\vec{D}$ = direction vector. I also have a spherical lens with aperture ...
1
vote
1answer
71 views

What is the normal form for this line?

I have calculated the parametric form of a line as: $L = P_1 + tP_1P_3 = <2,2,0> + t<1,2,2>$. If I am given a point $ K = <1,-1,-1>$, how would I show the normal form of plane $E$ ...
0
votes
1answer
61 views

3D Surface parametrization basics

I'm studying 3D rendering: I have a surface and the points on the surface are given by some function f such that $p = f (u, v)$ Since I'm a newbie this is unclear to me: how can a function of u and v ...
1
vote
1answer
272 views

Doubt with parametric and symmetric equations

In the line through $P(0, 0, 0)$ and is perpendicular to $x=y-5$, $z=2y-3$, when we solve the equations and get the symmetric equations in order to find the vectors $V_1$ and $V_2$, why the normal ...
2
votes
3answers
15k views

Find the equation of the plane passing through a point and a vector orthogonal

I have come across this question that I need a tip for. Find the equation (general form) of the plane passing through the point $P(3,1,6)$ that is orthogonal to the vector $v=(1,7,-2)$. I would ...