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Let ABCD be a parallelogram such that v...

Let ABCD be a parallelogram such that ` vec A B= vec q , vec A D= vec p""a n d""/_B A D` be an acute angle. If ` vec r` is the vector that coincides with the altitude directed from the vertex B to the side AD, then ` vec r` is given by (1) ` vec r=3 vec q-(3( vec pdot vec q))/(( vec pdot vec p)) vec p` (2) ` vec r=- vec q+(( vec pdot vec q)/( vec pdot vec p)) vec p` (3) ` vec r= vec q+(( vec pdot vec q)/( vec pdot vec p)) vec p` (4) ` vec r=-3 vec q+(3( vec pdot vec q))/(( vec pdot vec p)) vec p`

A

`vecr=3vecq+(3(vecp.vecq))/(vecp.vecp)vecp`

B

`vecr =-vecq +(vecp.vecq)/(vecp.vecp)vecp`

C

`vecr = vecq -(vecp.vecq)/(vecp.vecp)vecp`

D

`vecb -((vecb.veca)/(veca.vecb))vecc`

Text Solution

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The correct Answer is:
B
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