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The diagonals of a parallelogram are given by A = 3i -4j -k and B = 2i +3j - 6k. Show that the parallelogram is a rhombus and determine the length of its sides and its angles.

The diagonals of a parallelogram are given by A = 3i -4j -k and B = 2i +3j - 6k. Show that the parallelogram is a rhombus and determine the length of its sides and its angles.

Grade:12th pass

2 Answers

Deepak Kumar Shringi
askIITians Faculty 4407 Points
4 years ago
in the rhoumbus diagonals are perpendicular so if you do dot product of A and B it will be equal to zero
Almaas
13 Points
3 years ago
Let the side be a. Let  x be the acute angle of the rhombus. Magnitude of the smaller diagonal is √26.
a^2+a^2+2a.a.cosx=26.......1
From 1/2.d1.d2, we get area as √1274/2
Area=a.a.sinx=√1274/2...........2
Solving 1 and 2, we get a=5√3/2

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