In a conventional (x, y, z) coordinate system in space, the points A = (1,1,1), B = (3,0,0), C = (0,4,3) and D = (2 , 3.2).
a) Show that the four points span a parallelogram P, set up a parameter representation for P, and determine the area of P.
For random k > 0, the vector v = (2, −1, k) is considered
b) Determine the volume (as a function of k) of the set of points swept by P,
when P is shifted in parallel with v.
hello I get answer k=1 but should be 2
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Answer:
sides of parallelogram
Step-by-step explanation:
ANSWER
Opposite sides of the parallelogram are parallel
It means the slope of the two sides are equal
Slope of line passing through two points=
x
2
−x
1
y
2
−y
1
Consider, Sides AB and CD
∴
3−1
6+2
=
5−3
10−2
2
8
=
2
8
Slope of AB= Slope of CD
Slope of BC =(
5−3
10−6
)=
2
4
Slope of AD =(
3−1
2+2
)=
2
4
∴ The slope of BC=Slope of AD
Opposite sides are parallel. It means it is a parallelogram.
solution
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