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For any vector vec a\ a n d\ vec b pro...

For any vector ` vec a\ a n d\ vec b` prove that `| vec a+ vec b|lt=| vec a|+| vec b|dot`

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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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