Answer :

Let A(–1, 2, 1), B(1, –2, 5), C(4, –7, 8) & D(2, –3, 4)


ABCD can be vertices of parallelogram only if opposite sides are equal.


i.e. AB = CD & BC = AD


Calculating AB


A ≡ (– 1, 2, 1) and B ≡ (1, – 2, 5)


Distance AB


Here,


x1 = – 1, y1 = 2, z1 = 1


x2 = 1, y2 = – 2, z2 = 5


Distance AB






Calculating BC


B ≡ (1, – 2, 5) and C ≡ (4, – 7, 8)


Distance BC


Here,


x1 = 1, y1 = – 2, z1 = 5


x2 = 4, y2 = – 7, z2 = 8


Distance BC





Calculating CD


C ≡ (4, – 7, 8) and D ≡ (2, – 3, 4)


Distance CD


Here,


x1 = 4, y1 = – 7, z1 = 8


x2 = 2, y2 = – 3, z2 = 4


Distance CD






Calculating DA


D ≡ (2, – 3, 4) and A ≡ (– 1, 2, 1)


Distance DA


Here,


x1 = 2, y1 = – 3, z1 = 4


x2 = – 1, y2 = 2, z2 = 1


Distance DA





Since AB = CD & BC = DA


So, In ABCD both pairs of opposite sides are equal.


Thus, ABCD is a parallelogram.


Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
caricature
view all courses
RELATED QUESTIONS :

Determine the poiRD Sharma - Mathematics

The length of theRD Sharma - Mathematics

Let (3, 4, -1) anRD Sharma - Mathematics

The length of theRD Sharma - Mathematics

If P (0, 1, 2), QRD Sharma - Mathematics

Show that the triMathematics - Exemplar

Write the length RD Sharma - Mathematics

If the distance bRD Sharma - Mathematics

Find the point onRD Sharma - Mathematics

Find the point onRD Sharma - Mathematics