1.

What is geometrical significance of the relation |veca+vecb| = |veca-vecb|

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Solution :
Let ABCD be a PARALLELOGRAM where `vec(AB) = veca, vec(BC) = vecb`
Then `vec(AC) = veca+vecb`
Again `vec(AD) = vecb`
So `vec(DB) = veca-vecb`
Now AC = `|vec(AC)| = |veca+vecb|`
DB = `|vec(DB)| = |veca-vecb|`
If `|veca+vecb| = |veca-vecb|` then AC = DB.
Thus ABCD is a parallelogram where TWO diagonals are equal.
Hence ABCD must be a TECTANGLE with adjacent vectors `veca` and `vecb`.


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