1.

If (veca + vecb).(veca-vecb) = 0 show that |veca| = |vecb|.

Answer»

SOLUTION :`(veca+vecb).(veca-vecb) = 0`
`implies veca.(veca-vecb)+vecb(veca-vecb) = 0`
[because DOT product is distributed over VECTOR addition.]
`implies veca.veca-veca.vecb+vecb.veca-vecb.vecb = 0`
`implies veca.veca-vecb.vecb = 0 [because vecavecb = vecb.veca = 0]`
`implies |veca|^2 = |vecb|^2 implies |veca| = |vecb|` (Proved)


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