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