COORDINATE GEOMETRY
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Please help solve the following and show all work please. Thank you!

1.) Find the center and radius of the sphere x^2+y^2+z^2-2x+4z-4=0

2.) Find the projection of PQ onto PR given the points P(-1,2,4), Q(3,0,-2), and R(-5,-3,6)

3.) Find the initial point of vector u=<3,-2,11>, if the terminal point is B(-6,2,-1)

4.) Find the work done as a force F=<-4,2,8> moves an object from point P(9,-1,-3) to Q(2,4,-5).

5.) Write the equation of the plane containing the points P(-5,5,0), Q(3,3,0), and R(-4,-1,-5)

1…..
[X-1]^2+Y^2+[Z+2]^2=4+1+4=9
HENCE CENTER OF SPHERE IS [ 1 , 0 , - 2 ]
AND RADIUS = 3 UNITS
2…………….
P	-1	2	4
Q	3	0	-2
R	-5	-3	6
PQ=Q-P=	4	-2	-6
PR=R-P=	-4	-5	2
PROJECTION OF PQ ON TO PR = [{PQ.PR}/|PR|]*PR
PQ.PR= -16+10-12=-18
|PR|=[16+25+4]^0.5 = 45^0.5=			6.708204
PROJECTION OF PQ ON TO PR =			-2.68328	*[ - 4 , - 5 , 2 ]
3……
U=	3	-2	11
B=	-6	2	-1
I=B-U=	-9	4	-12
INITIAL POINT IS [ - 9 , 4 , - 12 ]
4…..
F=	-4	2	8
P=	9	-1	-3
Q=	2	4	-5
PQ=Q-P=	-7	5	-2
WORK DONE = F.[PQ]=28+10-16=22
5…..
P=	-5	5	0
Q=	3	3	0
R=	-4	-1	-5
EQN. OF PLANE THROUGH Q IS
A[X-3]+B[Y-3]+CZ = 0 ………………………………….1
PUTTING P & R IN THIS …
-8A+2B=0…………………B=4A
-7A-4B-5C=0……5C=-23A…..C=-4.6A
HENCE EQN. OF PLANE IS …
[X-3]+4[Y-3]-4.6Z=0
X+4Y-4.6Z=15
5X+20Y-23Z=75………….ANSWER