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If vec a , vec b are any two vectors, t...

If ` vec a , vec b` are any two vectors, then give the geometrical interpretation of relation `| vec a+ vec b|=| vec a- vec b|`

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Let OA=a and AB=b. completing the parallelogram OABC.

Then, OC=b and CB=a
from `DeltaOAB`, we have
`OA+AB=Obimpliesa+b=OB` . . . (i)
From `DeltaOCA,` we have
`OC+CA=OA`
`impliesb+CA=aimpliesCA=a-b` . . . (ii)
Clearly, `|a+b|=|a-b|implies |OB|=|CA|`
Diagonals of parallelogram OABC are qual.
OABC is a rectangle.
`implies OA bot OC implies a bot b`.
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