If a point on the surface of a sphere with its center at the origin has coordinates (9,4,6) how do you show the radius connecting the origin to this point as a position vector. Is it simply [9,4,6] or is it more complicated than that. Thanks.
If the sphere's centre is at the origin, then the vector from the origin to the point is simply (9,4,6) as you stated.
If the vector is from a point (x0,y0,z0) to the given point, then it is
(9-x0, 4-y0, 6-z0).
So when (x0,y0,z0)=(0,0,0), it reduces to simply (9,4,6).
Thanks!
To find the position vector connecting the origin to a point on the surface of a sphere, you need to subtract the coordinates of the origin from the coordinates of the point. In this case, the origin has coordinates (0,0,0) since it is the center of the sphere.
So, to find the position vector, you subtract the coordinates of the origin from the coordinates of the given point:
(9,4,6) - (0,0,0) = (9,4,6)
Therefore, the position vector connecting the origin to the point (9,4,6) on the surface of the sphere is indeed [9,4,6].