# Tagged Questions

The (3d) tag is for things related to 3-dimensions. For geometry of 3-dimensional solids, please use instead (solid-geometry). For geometry that is not on a plane, but otherwise agnostic of dimensions, perhaps (euclidean-geometry) or (analytic-geometry) should also be considered.

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### Equation of a plane passing through a point

Write an equation of the plane with normal vector n=<-6, 9, -8> passing through the point (-1, 3, 4) in scalar form. The equation should equal 2. I just learned this topic and I am having ...
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### Plane in 3 Dimensions

I just learned this topic and I'm having trouble with this homework problem... Find an equation of the plane through the three points given: $P = (0, 2, 0)$ $Q = (-4, 6, 2)$ $R = (3, 3, -1)$ The ...
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### Rotation rate around one axis transformed to a different axis at an angle to the first

Suppose I have a motor with axis M on my diagram rotating at rate $r$ [rad/sec]. Connected to the motor is a gyroscope, the axis G of which is at an angle a to to that of the motor (the gyroscope will ...
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### Find normal vector of circle in 3D space given circle size and a single perspective

I don't really know what to search up to answer my question. I tried such things as "ellipse matching" and "3d circle orientation" (and others) but I can't really find much. But anyways... I have ...
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### How do I do the math necessary to make these five matrices multiplied together equal the result shown?

I'm currently studying the math involved with rotating vertices around an arbitrary axis in 3D space. For this, I have found the following page to be very helpful: http://inside.mines.edu/~gmurray/...
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### Why is tree traversal the fastest ray-box method?

I'm learning ray tracing (the problem of intersecting a ray, aka a vector, against a 3D box defined by a max and a min point) and I'm wondering: why is a tree traversal (e.g. bounding volume ...
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### How to rotate a 3d vector to be parallel to another 3d vector using quaternions?

I have a vector (a,b,c) and another vector (d,e,f). I'm trying to rotate (a,b,c) so its parallel to (d,e,f) using quaternions. I need help understanding how I would do this. I have so far that a ...
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### Find vector rotated on 3D plane

I don't have access to a computer so I can't give pictures but I will try to make this easy to visualize. Suppose I have a vector $n$. I will now draw a plane normal to this vector that and have that ...
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### clockwise or counter clockwise in 3D

I have two different situation that I need to make distinction between them (shown in the picture). In other words, in (A) points 3 and 4 are in right and left side of line 1-2. However, in case (B) ...
I would like to know how one would find a point from the angles of three axes and a magnitude. I know how to do this in 2D: $(\cosΘ * m, \sin(Θ) * m)$. However, I would like to know how this would be ...