0
votes
1answer
16 views

Heading vector from angle (generated by trig) does not have expected result

I am creating a game and when the player taps on the screen, it should generate a ‘pulse’ effect, pushing away the player. For example, the heading vector should have negative x and y values when to ...
0
votes
2answers
57 views

Find the resulting speed and direction. Trig Problem involving resultant and vectors.

A barge is pulled by two tugboats. The first tugboat is traveling at a speed of 15 knots with heading 130°, and the second tugboat is traveling at a speed of 11 knots with heading 190°. Find the ...
0
votes
1answer
60 views

Problem involving Bearing, Heading, and True Course.

A plane is flying with an airspeed of 170 miles per hour and heading 150°. The wind currents are running at 30 miles per hour at 170° clockwise from due north. Use vectors to find the true course and ...
0
votes
1answer
79 views

Calculating accelerometer vector when tilted

I'm trying to develop a 3D position estimation program using an xyz accelerometer. Ignoring the massive error introduced by double integration of the acceleration to get displacement, I have another ...
0
votes
0answers
11 views

Get Attitude from 2-axis vector

I've built a quadrotor but my 3-axis accelerometer has a fault, the Z-Axis doesn't work. I would normally get my attitude with the following code pitch = atan2(accel_X, accel_Z)*RadToDeg; roll= ...
0
votes
0answers
27 views

How to find optimal perpendicular axis of rotation vector?

I am drawing lines on the screen. Each line has a point (x,y,z) and a direction (u,v,w). I want to draw arrow heads on these ...
-1
votes
1answer
90 views

How to draw arrows by rotating lines in 3d space?

I am trying to figure out direction vectors of the arrowheads of an arrow. Basically I'm given a normalized direction vector ...
0
votes
2answers
62 views

Is there a Taylor series for vector cross product?

I have this equation, where $u,v,w,a,b,Ɵ$ are constants. The RHS comes from the Geometric definition of the LHS $(u,v,w)(a,b,c)=||(u,v,w)||||(a,b,c)||\cos(\theta)$ Expanding the 2-norms ...
0
votes
2answers
46 views

Show that the functions are vectors.

Let $V$ be the subspace of $C^1(\mathbb R)$ spanned by $f(x) = \sin x $ and $g(x) = \cos x$. a) Show that for any constant value of $\theta$, the functions $f_1(x)=\sin (x+ \theta) $ and $f_2(x)= ...
1
vote
3answers
34 views

Find the unit normal $N$

of ${\bf r}=14 \mathrm{e}^{-10 t}\cos(t){\bf i}+14 \mathrm{e}^{-10 t}\sin(t){\bf j}$ The answer should be in vector form. I can't find an easy way to do this. I end up with T being something ...
0
votes
1answer
92 views

Converting from spherical coordinates to cartesian around arbitrary vector $N$

So if I'm given an arbitrary unit vector $N$ and another vector $V$ defined in spherical coordinates $\theta$ (polar angle between $N$ and $V$) and $\phi$ (azimuthal angle) and $r = 1$. How do I ...
2
votes
2answers
79 views

Angle between vectors of the form $(\cos A,\cos B,\cos C)$

The question: Two vectors $S=(\cos A,\cos B,\cos C)$, $S'=(\cos A',\cos B',\cos C')$, What is the angle between them? The answer is $\cos(\theta)$ = $\cos A.\cos A'+ \cos B.\cos B'+ \cos C.\cos C'$. ...
0
votes
0answers
20 views

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 ...
0
votes
1answer
79 views

Signed angle between 2 vectors?

http://stackoverflow.com/questions/2150050/finding-signed-angle-between-vectors on this link I found the following formula: ...
0
votes
0answers
26 views

Find vector with simple trigonometry

I've spent too much time solving a fluid mechanics problem because of this trigonometry. How do I find $V_{t2}$ ? The answer is $rw - V_{n2} \cot(\theta)$. (can't seem to get equations to work)
3
votes
1answer
1k views

Calculate Camera Pitch & Yaw To Face Point

How do you calculate pitch & yaw for a camera so that it faces a certain 3D point? Variables Camera X, Y, Z Point X, Y, Z Current Half Solution Currently I know how to calculate the pitch, ...
1
vote
1answer
734 views

Calculate Triangle Ground using Height and Top Angle

Is it possible to calculate the ground of a triangle only using the height and top angle. Click here to see a poorly draw sketch of what I'm trying to calculate. So is it possible and how, to ...
1
vote
1answer
96 views

Calculating mean velocity of an orbiting body as it moves towards a point.

I'm making a game, in the game planets orbit a central point in circular orbits, they move directly towards their targets and the vector is simply added to their orbital path. Whilst not realistic it ...
0
votes
2answers
26 views

Magnitude of Axis vectors in question

I have a question on my revision sheet: Write the vector, v=-2 i + 4 j , in polar form. is it safe to assume axis vectors i and j have a magnitude of 1?
0
votes
1answer
86 views

What is required to establish the law of cosines?

In my quantum computation course, we have been given nothing more than the basic axioms of a linear vector space, and and the properties of an inner product; but we have started referring to "the ...
2
votes
2answers
96 views

Duplicate quadratic Bézier curve with new start point?

I have Bézier curve as shown by the wikipedia gif here: I would like to create a new curve that is a segment of the old one. For example, in this gif (from the same article): .. if I wanted B to ...
2
votes
1answer
34 views

What is the length of a vector after it's components have been squared?

So if $c$ is the length of $(a,b)$ , and $f$ is the length of $(a^2,b^2)$ How do $c$ and $f$ relate? Or is it impossible?
2
votes
2answers
213 views

$W = T_1 \cos^2(\theta) + T_2 \sin^2(\theta)$ solve for $\theta$

If I have $W = T_1 \cos^2(\theta) + T_2 \sin^2(\theta)$ where $W,~ T_1$ and $T_2$ are all $3D$ vectors that all lie on the same plane, how do I rearrange this equation to get theta by itself?
0
votes
1answer
106 views

Vector Math and Directional Vectors

Short and sweet. How does one calculate a directional vector in 3 dimensions by knowing the magnitude of the vector and the rotations about both the x and y axis?
3
votes
1answer
540 views

How to plot N points on the surface of a D-dimensional sphere roughly equidistant apart?

Let's say I have a D-dimensional sphere with a radius R. I want to plot N number of points evenly distributed (equidistant apart from each other) on the surface of the sphere. It doesn't matter where ...
3
votes
2answers
7k views

Convert angle (radians) to a heading vector?

I have been looking everywhere trying to find out how to convert an angle in radians (expressed as -Pi to Pi) to a heading vector. The only [x,y] answer I have found is, [cos(angle), sin(angle)] , ...
1
vote
1answer
124 views

Given an exact velocity and a “velocity range”, what is the relative velocity range?

I'm trying to calculate the relative velocity ($V_R$) between an exact velocity ($V_0$) and a velocity range ($V_1$). The exact velocity ($V_0$) is represented simply by ($course$, $speed$). The ...
5
votes
2answers
743 views

Power-reduction formula

According to the Power-reduction formula, one can interchange between $\cos(x)^n$ and $\cos(nx)$ like the following: $$ \cos^n\theta = \frac{2}{2^n} \sum_{k=0}^{\frac{n-1}{2}} \binom{n}{k} ...
0
votes
1answer
110 views

A computation with vectors

I'm going through these lecture notes, and I don't understand how one of the example problems was solved. Can anyone show me a step by step solution? Question: Suppose a Canada goose is flying ...
0
votes
1answer
963 views

Finding a result vector from 2 vectors without cross product

If I have 2 lines with its symmetric equations I can get the vectors U and V of each line, and with a cross product I can get the vector R; but how can I get the vector R without a cross product?
2
votes
1answer
463 views

Tricky Lighthouse (well, tricky for me (a fool))— Finding Maximum Angle of Elevation

Here's the problem I'm stuck on. I'm honestly not even sure what it's asking. "The axis of a light in a lighthouse is tilted. When the light points east, it is inclined upward at 1 degree(s). When it ...
3
votes
1answer
804 views

How to find angle of motion in frictionless space based on vx and vy

This might, perhaps, be more suited to Stack Overflow or the Gaming section, but since it's math that is above my head, I thought I'd come straight here for it. I'm making a space game. So far I ...
0
votes
1answer
193 views

quaternion to angle

Alright, so this is how I am doing it: ...
1
vote
1answer
151 views

Getting the % that a point is on a line

Alright, so I got two points in 3d space, so they have a x,y, and z. Now if the line's y - which I get like so: ...
-2
votes
1answer
967 views

getting the x,y, and z angle of two points?

Alright, so I got two vectors that each contain a x y and z. We'll call them a and b. ...