A) parallelogram, which is neither a rhombus nor a rectangle
B) square
C) rectangle but not a square
D) rhombus but not a square
Correct Answer: A
Solution :
\[PQ=6i+j\], \[QR=-i+3j\], \[SR=6i+j\], \[PS=-i+3j\], \[PQ||BR\]and \[QR||PS\] |
PQRS is a parallelogram |
\[PQ.QR=\left( 6i+j \right)\left( -i+3j \right)\] |
\[=-6+3\] |
\[=-3\ne 0\] |
\[\therefore \] PQRS is not a rectangle. |
\[|PQ|=\sqrt{36+1}=\sqrt{37}\] |
\[|QR|=\sqrt{1+9}=\sqrt{10}\] |
\[|PQ|\,\,\,\,=\,\,\,|QR|\] |
\[\therefore \]It is not a rhombus. |
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