Question

I am working on homework for a day i missed and have a few questions. ill put them all in one question here.
1. how do i find distance between p1 and p2?
P1=(-2,2,3) P2=(4,0,-3)

2. Write v in the form ai+bj+ck
P=(-3,2,0) Q=(6,5,-1)

3. find IIvII

v=-6i+12j+4k

4. write v in the form ai+bj and find IIvII

P=(-3,1) Q=(4,-2)

Answer 1

moving the points so that one of the is at the origin, makes life simpler to find distance

Answer 2

zero out one point, and what you do to one of them, to do all of them

P1=(-2,2,3) P2=(4,0,-3)
2-2-3 2-2-3
-------------------
0 0 0 6 -2 -6

square add sqrt the non zero point

Answer 3

in general:
P1=(a,b,c) P2=(x,y,z)
-a-b-c -a-b-c
---------------------
0 0 0 x-a,
y-b,
z-c

(x-a)^2 + (y-b)^2 + (z-c)^2

\[\sqrt{(x-a)^2 + (y-b)^2 + (z-c)^2}\]

Answer 4

Im still not sure i understand is that how you got the 6 -2 -6?

Answer 5

all i did was move the setup to the origin; consider the 2 points ive drawn here


moving them does not change the property of length between them ....