Q. 64.3( 4 Votes )

# Prove that the di

Answer :

Given:- Rhombus OABC i.e all sides are equal

To Prove:- Diagonals are perpendicular bisector of each other Proof:- Let, O at the origin

D is the point of intersection of both diagonals be position vector of A and C respectively

Then,  Now,  as AB = OC ……(i)

Similarly  ……(ii)

Tip:- Directions are important as sign of vector get changed

Magnitude are same AC = OB = √a2 + c2

Hence from two equations, diagonals are equal

Now let’s find position vector of mid-point of OB and AC  and  Magnitude is same AD = DC = OD = DB = 0.5(√a2 + c2)

Thus the position of mid-point is same, and it is the bisecting point D

By Dot Product of OB and AC vectors we get,    As the side of a rhombus are equal OA = OC  Hence OB is perpendicular on AC

Thus diagonals of rhombus bisect each other at 90°

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