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Vectors and Complex Numbers

Quick questions on The vector (cross) product explained: H2 Mathematics Vectors and Complex Numbers

5short Q&A pairs drawn directly from our worked dot-point answer. For full context and worked exam questions, read the parent dot-point page.

What is a perpendicular vector?
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Because a×b\mathbf{a} \times \mathbf{b} is perpendicular to both, it is the natural way to find a normal vector to a plane through two direction vectors, used heavily in plane equations.
What is sign error in the middle component?
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The j\mathbf{j} component is a3b1−a1b3a_3 b_1 - a_1 b_3 (note the order); the determinant expansion introduces a sign that is easy to drop.
What is q1?
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Compute (100)×(010)\begin{pmatrix} 1 \\ 0 \\ 0 \end{pmatrix} \times \begin{pmatrix} 0 \\ 1 \\ 0 \end{pmatrix}. [2 marks]
What is q2?
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State what the magnitude of a×b\mathbf{a}\times\mathbf{b} represents geometrically. [1 mark]
What is q3?
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Explain why the cross product is useful for finding a normal to a plane. [2 marks]

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