Need Help With a 4u Vector Question Ty (1 Viewer)

notme123

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i)
So the cartesian equation form of a sphere is where the centre is (a,b,c) with radius r.
Your centre for S1 is (2,2,2) and your radius is the distance between the centre and the given point that the sphere passes through i.e.
Therefore, the cartesian equation is

ii) Notice with S2 that it is displaced exactly 3 units above S1. Hence, the circle intersection created will be perfectly on the x-y plane.
Using the two cartesian equations, simply subtract S2 from S1. Here, the terms will cancel. You'll be left with:
.
Solve this and you'll find
Therefore, the centre of the circle is (2,2,16/3)
Simply sub this z coordinate back into one of the Sphere equations and you'll find:

This immediately tells us that the radius of the circle is

Thus your equation in full would be AND
 

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