Section 1.2: 3D Coordinate System
Problem types
Points on a line
Do the following points lie on a straight line? Explain.
$$P_1 = (1,2,1), P_2 = (1,1,1), P_3 = (3,3,2)$$
Solution
Circles and Spheres
Draw the equation $x^2+y^2 = 1$ in the 2D plane.
Solution
Now draw it again in 3D space.
Solution
Spheres!
Find the sphere with center $$C=(1,1,1)$$ that goes through the point $$P=(3,3,2).$$
Solution
More Spheres
Find the radius $r$ of the sphere $C_1$ centered at $(a,0,0)$ so that $C_1$ intersects $C_2: x^2+y^2+z^2 = 25$ at $x = 3$.
For which values of $a$ can this occur?
What changes if we take $C_2: x^2+y^2+z^2 = A^2$ instead?
Solution
More Spheres
Find the radius $r$ of the sphere $C_1$ centered at $(a,0,0)$ so that $C_1$ intersects $C_2: x^2+y^2+z^2 = 25$ at $x = 3$.
What changes if we take $C_2: x^2+y^2+z^2 = A^2$ instead?
Solution