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Question
Let P,Q,R and S be the points on the plane with position vectors −2^i−^j,4^i,3^i+3^j and −3^i+2^jrespectively. The quadrilateral PQRS must be a
Let P,Q,R and S be the points on the plane with position vectors −2^i−^j,4^i,3^i+3^j and −3^i+2^jrespectively. The quadrilateral PQRS must be a
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Solution
The correct option is A Parallelogram, which is neither a rhombus nor a rectangle
Let O be the origin,
then −−→OP=−2^i−^j
−−→OQ=4^i
−−→OR=3^i+3^j
−−→OS=−3^i+2^j
Here we have
−−→PQ=6^i+^j
−−→QR=−^i+3^j
−−→RS=−6^i−^j
and −→PS=−^i+3^j
−−→PR=5^i+4^j
−−→QS=−7^i+2^j
−−→PR.−−→QS=−35+8=−27≠0
Diagonals are not perpendicular
and ∣∣∣−−→PQ∣∣∣=∣∣∣−−→RS∣∣∣,∣∣∣−−→QR∣∣∣=∣∣∣−→PS∣∣∣
Hence PQRS is a parallelogram which is neither a rhombus nor a rectangle.
Let O be the origin,
then −−→OP=−2^i−^j
−−→OQ=4^i
−−→OR=3^i+3^j
−−→OS=−3^i+2^jHere we have
−−→PQ=6^i+^j
−−→QR=−^i+3^j
−−→RS=−6^i−^j
and −→PS=−^i+3^j
−−→PR=5^i+4^j
−−→QS=−7^i+2^j
−−→PR.−−→QS=−35+8=−27≠0
Diagonals are not perpendicular
and ∣∣∣−−→PQ∣∣∣=∣∣∣−−→RS∣∣∣,∣∣∣−−→QR∣∣∣=∣∣∣−→PS∣∣∣
Hence PQRS is a parallelogram which is neither a rhombus nor a rectangle.
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