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Vectors and Complex Numbers

Quick questions on Lines in 3D explained: H2 Mathematics Vectors and Complex Numbers

7short 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 the vector equation of a line?
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A line through a point with position vector a\mathbf{a} in the direction d\mathbf{d} is
What is the Cartesian form?
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Eliminating λ\lambda from the components gives the symmetric Cartesian equations:
What are classifying a pair of lines?
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The angle between two lines comes from the dot product of their direction vectors.
What are angle from position vectors?
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The angle between lines uses the direction vectors, not the points on them.
What is q1?
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Write the vector equation of the line through (2,−1,4)(2, -1, 4) in direction (103)\begin{pmatrix} 1 \\ 0 \\ 3 \end{pmatrix}. [2 marks]
What is q2?
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State the condition for two lines to be parallel. [1 mark]
What is q3?
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Explain how to tell, after solving for λ\lambda and μ\mu, whether two non-parallel lines intersect. [2 marks]

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