Area of parallelogram using vector product

A question is this type if and only if it asks to find the area of a parallelogram or rhombus given edge vectors, using the vector product.

2 questions · Standard +0.3

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Edexcel Paper 1 2022 June Q9

6 marks Standard +0.3

9. \begin{figure}[h]

\includegraphics[alt={},max width=\textwidth]{129adfbb-98fa-4e88-b636-7b4d111f3349-20_406_515_246_776} \captionsetup{labelformat=empty} \caption{Figure 3}

\end{figure} Figure 3 shows a sketch of a parallelogram \(P Q R S\).
Given that

\(\overrightarrow { P Q } = 2 \mathbf { i } + 3 \mathbf { j } - 4 \mathbf { k }\)
\(\overrightarrow { Q R } = 5 \mathbf { i } - 2 \mathbf { k }\)
1. show that parallelogram \(P Q R S\) is a rhombus.
2. Find the exact area of the rhombus \(P Q R S\).

OCR Further Additional Pure AS Specimen Q2

5 marks Standard +0.3

2 The points \(A ( 1,2,2 ) , B ( 8,2,5 ) , C ( - 3,6,5 )\) and \(D ( - 10,6,2 )\) are the vertices of parallelogram \(A B C D\). Determine the area of \(A B C D\).