If A(1,-3,2) find the coordinates of two points which are equidistant from A and have the magnitude of 5?
2 Answers
Explanation:
Let one point be
Distance between
Substitute arbitrary values for
We can do this, since we are not restricted to any line or plane.
Let
and the other point be
Then:
Co-ordinates of the 2 points are:
Notice that we had
PLOT:
See below.
Explanation:
Another way of seeing this problem.
All points equidistant from some given point in 3 dimensional space lie on the surface of a sphere.
The general equation of a sphere is given as:
Where:
If
will lie on the surface of the sphere and be 5 units from the centre.
So assigning arbitrary values to two of the variables and calculating the third will be solutions.
Let.
Two points are:
We could write a general solution as:
With
PLOT: