Parallelogram in vector?

Question

Parallelogram in vector problem?
Point A,B,C and D form a parallelogram in three dimensions, with point A (3,2,5), point B (2,1,3), point C (x,y,z) and point D (4,6,8). |AB| = |CD| and |BC| = |DA|

Find the coordinates of point C.

Answer 1

Because |AB| = |CD| and because the AB is parrallel to CD, it follows that the vector formed from A to B is the same as the vector formed from C to D. So, vector B - A should give the same results as C - D You can see this better by drawing a picture and noting that B shares a side with A and C and is opposite from D.

So, (2, 1, 3) - (3, 2, 5) = (x, y, z) - (4, 6, 8) or
C = (3, 5, 6)

Answer 2

AB = B - A = B(2,1,3) - A(3,2,5) = <-1, -1, -2>
DC = C - D = C(x,y,z) - D(4,6,8) =

x - 4 = -1
y - 6 = -1
z - 8 = -2

C(x,y,z) = (3, 5, 6)

AD = D - A = D(4,6,8) - A(3,2,5) = <1, 4, 3>
BC = C - B = C(x,y,z) - B(2,1,3) =

x - 2 = 1
y - 1 = 4
z - 3 = 3

C(x,y,z) = (3, 5, 6)

We get the same answer both ways as we would expect.

Answer 3

OP = A + B is any factor P such that P lies interior the paralleogram. A and B are constants such that P(x, y, z) continually lies interior the bigger parallelogram. So, A has to lie between 0 and a million inclusive B has to lie between 0 and a million inclusive. while A and B the two equivalent a million then OP = OPo(xo,yo,zo) = a million + a million that's approximately it i think of. desire it helps....

Answer 4

parallelogram can have only two dimensions, always!!!

Answer 5

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