Question

Given the three points A(−1,5,5),B(0,9,9),C(17,20,18), let: - S1 be the sphere with centre A and radius 10 ,

- S2 be the sphere which has the line segment BC as a diameter,
- T be the circle of intersection of S1 and S2,
- E be the centre of T,
- L1 be the line through B and E,
- L2 be the line through A parallel to (3 4 4 ) Using the geom3d package, or otherwise:
(i) Find the coordinates of E

Answer 1

To find the coordinates of E, calculate the intersection of spheres S1 centered at A with radius 10, and S2 with diameter BC, then find the midpoint of the arc of intersection.

Step-by-step explanation:

The student has asked to find the coordinates of E, the center of the circle T which is the intersection of two spheres S1 and S2. The first sphere S1 has its center at point A and a radius of 10 units. The second sphere S2 has its diameter defined by the line segment BC. To find the coordinates of E, one must determine the points of intersection between the two spheres and then find the center of that circle of intersection.

While the specific method for finding E is not detailed in the question, a common approach involves setting up the equations of the spheres and solving for their intersection points. From there, the coordinates of E can be determined by calculating the midpoint of the arc created by those intersection points.