Re: Vector calculus question

It is easy

in the plane this equation represents a circle.

in the 3d it will be a sphere. Put M(x,y,z) find the vectors AM and MB and get their scalar product....the rest is easy.

Re: Vector calculus question

OK. So ive taken the scalar prodcut and get:

But what next?

Re: Vector calculus question

No, that's incorrect. Taking the ordinates of point M to be , the vectors AM and BM are and respectively. The dot product is .

Re: Vector calculus question

Quote:

Originally Posted by

**HallsofIvy** No, that's incorrect. Taking the ordinates of point M to be

, the vectors AM and BM are

and

respectively. The dot product is

.

How do you get the sign to be negative for the terms ?? Thats not how the above parenthesis expands?

Re: Vector calculus question

Hello, FelixHelix!

Let

Then: .

We have: .

. .

. .

. .

Complete the square:

. .

. . . . . .

. .

The locus of M is a sphere with center

. . and radius:

Re: Vector calculus question

Then: . the vector isnt BM but MB. Will this matter?