Specialist Mathematics Β· Unit 3 Β· Vectors in two and three dimensions Β· Vector and Cartesian equations

Define and use the vector (cross) product to determine a vector normal to a given plane, with and without technology. 𝒂 Γ— 𝒃 = |𝒂| |𝒃| sin(πœƒ) 𝒏̂ 𝒂 Γ— 𝒃 = ( π‘Ž1 π‘Ž2 π‘Ž3) Γ— ( 𝑏1 𝑏2 𝑏3) = ( π‘Ž2𝑏3 βˆ’ π‘Ž3𝑏2 π‘Ž3𝑏1 βˆ’ π‘Ž1𝑏3 π‘Ž1𝑏2 βˆ’ π‘Ž2𝑏1)

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Determine vector, parametric and Cartesian equations of straight lines and straight-line segments given the position of two points, or equivalent information, in both two and three dimensions. vector equation of line: 𝒓 = 𝒂 + 𝑑𝒅 parametric equations of line: π‘₯ = π‘Ž1 + 𝑑 𝑑1 𝑦 = π‘Ž2 + 𝑑 𝑑2 𝑧 = π‘Ž3 + 𝑑 𝑑3 Cartesian equation of line: π‘₯βˆ’π‘Ž1 𝑑1 = π‘¦βˆ’π‘Ž2 𝑑2 = π‘§βˆ’π‘Ž3 𝑑3
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