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August 28, 2016
Posted by **Melinda** on Friday, March 23, 2012 at 4:03pm.

a) what are the location of the vertices?

b) what are the vectors representing the diagonals?

c) what are the length of the diagonals?

- Calculus and vectors -
**MathMate**, Friday, March 23, 2012 at 4:46pm(a)

Parallelogram: PACB, where

P(0,2,3) is a vertex.

A=P+PA=(0,2,3)+(3,2,-3)=A(3,4,0)

B=P+PB=(0,2,3)+(4,1,5)=B(4,3,8)

C=A+PB=(3,4,0)+(4,1,5)=C(7,5,5)

(b)

PC=C-P=(7,5,5)-(0,2,3)=(7,3,2)

AB=B-A=(4,3,8)-(3,4,0)=(1,-1,8)

Lengths

PC=sqrt(7²+3²+2²)=sqrt(49+9+4)=√62

I leave you to find the length of AB in a similar way to finding length of PC.