Q. 45.0( 1 Vote )

# Prove by vector m

Given:- Parallelogram OABC

To Prove:- AC2 + OB2 = OA2 + AB2 + BC2 + CO2

Proof:- Let, O at origin

Therefore,

Distance/length of AC

By triangular law:-

the the vectors form sides of triangle

As AB = OC and BC = OA

From figure

……(i)

Similarly, again from figure

……(ii)

Now,

……(iii)

Take RHS

OA2 + AB2 + BC2 + CO2

……(iv)

Thus from equation (iii) and (iv), we get

LHS = RHS

Hence proved

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