Which octant/plane
Which octant/plane does (1, 1, 1) belong in
Octant 1 because all of the coordinates are positive
Find distance between (0, 0, 1) and (0, 0, 100)
99
Find center of the sphere: x^2+y^2+(z-1)^2=100
(0, 0, 1)
Find radius: (x-1)^2+(y-2)^2+(z+1000)^2=1
Determine whether the points make a straight line and show work
a) (1, -2, 3)
b) (4, 4, -3)
c) (6, 8, 7)
the pattern from a to b and b to c should stay consistent. To get to a to b, the 3-d vector would (3, 6, -6). To get to b to c, then vector is (2, 4, 10). Therefore, since pattern is inconsistent, this isn't collinear.
Which octant/plane is the (0, 0, 0)
None, it's the origin, duh...
What is the distance and midpoint between (1, 1, 1) and (1, 2, 3)
Distance= (0+1+4)^(1/2)=(5)^(1/2)
Midpoint= (1, 1.5, 2)
What is the center and radius: (x-100)^2+(y+99)^2-(z+0.01)^2=2.25
Center: (100, -99, -0.01)
Radius: 1.5
What is the distance between the center of the given sphere and the x-axis: (x-1.09)^2+(y-1000)^2+(z+256)^2=2500
the center is (1.09, 1000, 256.23). the x coordinate doesn't matter (since you're looking to compare with x-axis). Therefore, we have to find the distance between the axis with respect to only y and z. Therefore, d=((1000-0)^2+(-256-0)^2)^(1/2)=1032.248
Which octant/plane does (0, 5, 2)
the yz plane because there's no x coordinate