Any nonzero vector would be a normal at some point on the surface of the sphere. My guess is that you should take an arbitrary point P(x, y, z) on the surface, and find the normal to it. If that's what is wanted in the problem, it could have been written more clearly.Frozen Light said:Homework Statement
Consider a unit sphere centered at the origin. In terms of the Cartesian unit vectors i, j and k, find the unit normal vector on the surface
Homework Equations
A dot B = AB cos(theta)
A cross B = AB (normal vector) sin(theta)
Unit sphere radius = 1The Attempt at a Solution
Isn't any direction a normal vector?
i x j = + k
j x i = - k
etc.
To find a normal vector to a unit sphere using cartesian coordinates, you can use the equation n = (x, y, z) where x, y, and z are the coordinates of a point on the sphere's surface. This will give you a vector that is perpendicular to the surface of the sphere at that point.
The formula for a unit sphere in cartesian coordinates is x^2 + y^2 + z^2 = 1. This means that for any point on the sphere's surface, the sum of the squares of its x, y, and z coordinates will equal 1.
A normal vector is a vector that is perpendicular to a surface at a given point. In the case of a unit sphere, the normal vector at any point on its surface will be a vector that points directly away from the center of the sphere and has a length of 1.
Surface normal vectors are used to describe the orientation of a surface at a given point. In the case of a unit sphere, the normal vector at any point on its surface can be used as a surface normal vector to describe the orientation of the sphere's surface at that point.
Yes, a normal vector to a unit sphere can also be found using spherical coordinates or cylindrical coordinates. However, the cartesian coordinate system is the most commonly used method for finding a normal vector to a unit sphere.