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Figure 3 shows a sketch of a parallelogram PQRS - Edexcel - A-Level Maths Pure - Question 11 - 2022 - Paper 1
Question 11
Figure 3 shows a sketch of a parallelogram PQRS. Given that • egin{align*} ext{PQ} &= 2i + 3j - 4k\ ext{QR} &= 5i - 2k ext{(a)} & ext{ show that parallelogra... show full transcript
Worked Solution & Example Answer:Figure 3 shows a sketch of a parallelogram PQRS - Edexcel - A-Level Maths Pure - Question 11 - 2022 - Paper 1
Step 1
Final area calculation
Answer
Evaluating the determinant:
[
A = |\text{PQ} \times \text{QR}| = ext{det} = \mathbf{[4+10]i - [6+8]j + [0-15]k}\ \\
= 6i - 14j - 15k
]
Thus, the area will be:
[
A = \sqrt{6^2 + (-14)^2 + (-15)^2} = \sqrt{36 + 196 + 225} = \sqrt{457}
\approx 21.4
]
Therefore, the exact area of the rhombus PQRS is (\sqrt{457}\text{ or approximately } 21.4 \text{ square units}.