Spherical coordinates position vector

In summary, the question is asking for the position vector of points P and Q on a diameter perpendicular to the plane containing points U, V, and W on a unit sphere centered at the origin. The solution involves finding two planar vectors from the given position vectors and using the triple scalar product to find a vector perpendicular to those two.
  • #1
mickry
6
0
can anyone help me with this question:
A sphere of unit radius is centered at the origin. points U,V & W on the surface of the sphere have vectors u,v & w. find the position vector of points P&Q on a diameter perp to the plane containing points U,V & W?

can anyone help
 
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  • #2
In Cartesian coordinates if the points U, V, W are coplanar, to which position vectors u, v, w point, respectively, what can one do to create two planar vectors? Hint. What is the formula for the vector pointing from U to V? Similarly for V to W or U to W.

Now with two coplanar vectors, how does one find a vector perpendicular to those two?
 
  • #3
tripple scaler product?
 

FAQ: Spherical coordinates position vector

1. What is a spherical coordinates position vector?

A spherical coordinates position vector is a mathematical representation of a point in three-dimensional space using the distance from the origin, the inclination angle, and the azimuth angle.

2. How is a spherical coordinates position vector different from a Cartesian coordinates position vector?

A spherical coordinates position vector uses angles to represent position, while a Cartesian coordinates position vector uses length measurements along x, y, and z axes.

3. How do you convert a spherical coordinates position vector to a Cartesian coordinates position vector?

To convert a spherical coordinates position vector (r, θ, φ) to a Cartesian coordinates position vector (x, y, z), use the following equations:
x = r * sin(θ) * cos(φ)
y = r * sin(θ) * sin(φ)
z = r * cos(θ)

4. What is the significance of the inclination and azimuth angles in a spherical coordinates position vector?

The inclination angle (θ) represents the angle between the position vector and the positive z-axis, while the azimuth angle (φ) represents the angle between the projection of the position vector onto the xy-plane and the positive x-axis.

5. In what fields of science are spherical coordinates position vectors commonly used?

Spherical coordinates position vectors are commonly used in fields such as physics, astronomy, and geology to describe the position of objects in three-dimensional space, particularly when dealing with spherical or circular objects or systems.

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