Asked by Melinda
A parallelogram is formed by R^3 by the vectors PA=(3,2,-3) and PB=(4,1,5). The point P=(0,2,3).
a) what are the location of the vertices?
b) what are the vectors representing the diagonals?
c) what are the length of the diagonals?
a) what are the location of the vertices?
b) what are the vectors representing the diagonals?
c) what are the length of the diagonals?
Answers
Answered by
MathMate
(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.
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.
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