Asked by 100.akash | 16th Sep, 2008, 04:13: PM
let BP = CQ =b and side of square be a.
we have to prove AQ is perpendicular to DP.
in vector form AQ = AB + BQ
and DP = DA + AP
taking dot product of AQ and DP
=AB.DA + AB.AP +BQ.DA + BQ.AP
now AB & DA and BQ &AP are perpendicular to each other so there dot product will be zero.
=AB.AP + BQ.DA ( |AB|=|DA| = a , |BQ|=|AP| = a+b)
=a(a+b) - (a+b)a ( BQ and DA are in opposite direction so a negative sign comes)
since AQ.DP = 0 i.e. AQ and DP are perpendicular to each other.
Answered by | 18th Dec, 2008, 08:22: PM
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