# Tagged Questions

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### Dot product of any point on plane and its normal

I was trying to find the distance between a point and a 3D line with parametric equations. On the web, I found a video detailling the steps. https://www.youtube.com/watch?v=9wznbg_aKOo At 2:20, the ...
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### Translation of basis for a vector space on the specified distance

In the Euclidean space $XYZ$ is a basis $X_1Y_1Z_1$ defined that is specified by the vectors $\overrightarrow {O_1X_1}$, $\overrightarrow {O_1Y_1}$ and $\overrightarrow {O_1Z_1}$. How to calculate ...
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### Difference between Euclidean space and vector space?

I often hear them used interchangeably ... they are very complicated to make any use of. Wikipedia words: Euclidean space: One way to think of the Euclidean plane is as a set of points ...
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### number of planes possible such that it is equidistant from 4 non coplanar points

If there are for non coplanar points find the number of planes such that all four of them are equidistant from the plane . Sorry one of those problems where dont know what to do . How should i do this ...
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### Generating a 3d ribbon from a series of points

I am attempting to generate a 3d ribbon from a set of 3d points. The idea is to generate a realistic ribbon which follows those points. In its current state, one example looks like this: In this ...
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### Finding a point on a 3d line

I have two points in 3D which will create a single ray. I am trying to find a point on that ray which intersects a plane who's y coordinate is 0. So how do I find a point on a 3D line when I know the ...
131 views

### Getting angles for rotating $3$D vector to point in direction of another $3$D vector

I've been trying to solve this in Mathematica for $2$ hours, but got the wrong result. I have a vector, in my case $\{0, 0, -1\}$. I want a function that, given a different vector, gives me angles DX ...
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### Resolving bearings for tilted structure (vector rotations)

I am trying to find a neat solution to resolving bearings for a tilted structure. For example, if I know that a hub is $268.74^{\circ}$ and offset ($X = -3.542$m, $Y = -1.857$ m, $Z = 2.013$m) with ...
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### Finding the Y position of a point between four points on a plane in 3d space

I have been wracking my mind for a while about this... I recently created a function which would utilise Perlin noise to create a 3D pseudo-randomised landscape (and return it as a two-dimensional ...
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### sweeping edges till they get a given elevation on an oblique plane

I am constructing wireframe model of 3d objects (prisms,..etc.). from a triangular mesh, I have obtained boundary points and fit striaght lines in order to get polygon edges refering to prism ...
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### How to move a one 3D line from three 3d parallel lines

I have 3 parallel line segments (say AB, CD, and EF are line segments and they are nearly horizontal) lay on 2 slanted planes which have been intersected through the CD. If I projected all the line ...
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### Point on the left or right side of a plane in 3D space

I have an alpha plane determined by 3 points in space. How can I check if another point in space is on the left side of the plane or on the right side of it? I need a fast solution for plug-in ...
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### 3D Cartesian Coordinates System revolve around a specified axis

I have a 3d cartesian coordinates system and now I want to rotate a point $p(x_0, y_0, z_0)$ arround a specified axis $v(v_x, v_y, v_z)$ like $(1,1,1)$,and the angle is $\theta$,finally I want to get ...
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### particle with radius 'r' hits the plane. what is the point of contact?

A large particle with radius r hits the plane with perpendicular 'n' and passing through ,q'. I need to check whether it hits the plane or not. In order to do that I need to find the point of contact. ...
179 views

### Given velocity and position, when does it hit the plane?

A particle at position $p$ and velocity $\vec{v}=\langle x,y,z \rangle$ hits the plane orthogonal to vector $\vec{n}$ and passing through point $q$. When does the particle hit the plane? I calculated ...
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### How to recover three successive rotations of a vector

I have a vector, which I rotated with respect to $x$, $y$ and $z$ axes, respectively. Now I want to recover this operation, that means I want to bring it to the previous position by rotating it with ...
18k views

### Calculate Rotation Matrix to align Vector A to Vector B in 3d?

I have one triangle in 3d space that I am tracking in a simulation. Between time steps I have the the previous normal of the triangle and the current normal of the triangle along with both the current ...
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### Calculating angle of human joint beyond 180° in 3D

I'm having some trouble calculating the angle of an human joint in 3D using the Microsoft Kinect. Here's an example of the angle of the elbow (using the shoulder and wrist joint): Image of example ...
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### Can 2 parallel lines be discriminated as 'away', 'beside' with respect to 3rd parallel line?

I have nearly parallel several 3D line segments. some line segments locate (blue line) beside to a spefic line segment (black line) and some other (red line) locate away from that line segment. i want ...
712 views

### Extend angle between two 3D vectors to x-y plane.

I would like to know how I can extend the angle between two vectors in 3D space to the x-y plane. So, there are two vectors in 3D space, and the angle between them is found using the definition of ...
568 views

### line projection on top of a plane

If I have a horizontal line (a 3d point and 3d vector with zero z component) and another plane (could be an oblique or a horizontal; i have normal vector of the plane); then how do we get the ...
664 views

### Three-dimensional vectors and force systems

Full disclosure: this is a homework problem. However, I find myself stuck in the middle. The problem is below As shown, a system of cables suspends a crate weighing W = 350 . (Part C 1 figure) ...