I really didn't understand finding the determinants of a 3 X 3 or a 4 X 4. That stuff just blew my mind. I am going to go over the section that is labeled as 3-D.
- absolute value of vector AB= √(x2-x1)^2+(y2-y1)^2+(z2+z1)^2
- midpoint= (x1+x2/2, y1+y2/2, z1+z2/2)
- Equation of a sphere - (x-x0)^2+(y-y0)^2+(z-z0)^2= r^2
- Vector equation - (x,y,z)=(x0,y0,z0)+ t(a,b,c)
- vector addition, magnitude, dot product, all follow same formula with extra variable.
Ex. 1 A sphere has points A(8,-2,3) and B(4,0,7) as endpoints of the diameter.
a. Find the center and radius
b. Find an equation of the sphere.
A.) Center= (8+4/2, 0+-2/2, 7+3/2)
c=6,-1,5
√(4-6)^2+(0-(-1)^2+(7-5)^2= 9
√2^2+1^2+2^2= √9= 3
B.) Equation of the sphere - (x-6)^2+(y-(-1)^2+(z-5)^2=9
So, if you know the formulas for this section it will be pretty easy. I will look over them a few more times before the test, so that I know that I have them memorized. That's all for this blog.
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