Question: Prove that \vec{PQ} + \vec{QR} + \vec{RS} + \vec{SP} = 0 in the given quadrilateral PQRS.
Solution:
To prove: \vec{PQ} + \vec{QR} + \vec{RS} + \vec{SP} = 0
Construction: Join P and R.

Proof:
Using ∆ law of vector addition,
\vec{PR} = \vec{PQ} + \vec{QR} - (i)
Also,
\vec{RP} = \vec{RS} + \vec{SP} - (ii)
Taking LHS,
= \vec{PQ} + \vec{QR} + \vec{RS} + \vec{SP}
[Put value of \vec{PR} = \vec{PQ} + \vec{QR} from equation (i) ]
= (\vec{PR}) + \vec{RS} + \vec{SP}
[Put value of \vec{RP} = \vec{RS} + \vec{SP} from equation (ii) ]
= \vec{PR} + \vec{RP}
= \vec{PR} - \vec{PR}
= 0
RHS
#proved
0 Comments
You can let us know your questions in the comments section as well.