1.

If vec(a), vec(b), vec(c) are the position vectors of corners A, B, C or a parallelogram ABCD, then what is the position vector of the corner D?

Answer»

`VEC(a)+vec(B)+vec(C)`
`vec(a)+vec(b)-vec(c)`
`vec(a)-vec(b)+vec(c)`
`-vec(a)+vec(b)+vec(c)`

Solution :Let O be the ORIGIN and ABCD be the parallelogram.
In `DeltaODC`,
`vec(OD)=vec(OC)+vec(CD)`
`vec(CD) = - vec(AB)`
and, In `DeltaAOB, vec(AB)=vec(OB)-vec(OA)=vec(b)-vec(a)`
Thus, `vec(CD)=-vec(AB)=vec(a)-vec(b)`

So, `vec(OD)=vec(c)+vec(b)`[since, `vec(OC)=vec(C) and vec(CD)=vec(a)-vec(b)`]


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