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Engineering

Mathematics

Linear Combination of Vectors

Question

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rhombus, but not a square.

parallelogram, which is neither a rhombus nor a rectangle.

square.

rectangle, but not a square.

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P(–2, – 1); Q(4, 0); R (3, 3); S(–3, 2)

$m_{PQ} = \frac{0 - (- 1)}{4 - (- 2)} = \frac{1}{6}$ $m_{PR} = \frac{3 - (- 1)}{3 - (- 2)} = \frac{4}{5}$

$m_{RS} = \frac{2 - 3}{3 - 3} = \frac{1}{6}$ $m_{QS} = \frac{2 - 0}{- 3 - 4} = \frac{- 2}{7}$

$m_{PS} = \frac{2 - (- 1)}{- 3 - (- 2)} = - 3$ $m_{PR} \cdot m_{QS} \neq - 1$

$m_{QR} = \frac{0 - 3}{4 - 3} = - 3$ $∴$ not a rhombus

$∵ m_{PQ} \cdot m_{PS} = \neq - 1$ $∵$ not a rectangle or square

$∵$ PQRS is a parallelogram but not a rectangle or rhombus.

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