Specialist Mathematics Β· Unit 3 Β· Vectors in two and three dimensions Β· Vector and Cartesian equations
Understand and use equations of spheres. equation of sphere: (π₯ β β)2 + (π¦ β π)2 + (π§ β π)2 = π2
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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: π = π + π‘π
parametric equations of line: π₯ = π1 + π‘ π1 π¦ = π2 + π‘ π2 π§ = π3 + π‘ π3 Cartesian equation of line: π₯βπ1 π1 = π¦βπ2 π2 = π§βπ3 π3
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Use vector equations of curves in two or three dimensions involving a parameter, and determine a βcorrespondingβ Cartesian equation in the two-dimensional case.