Algebra of vectors in three dimensions
Specialist Mathematics · Unit 3 — Further complex numbers, proof, vectors and matrices · Vectors in two and three dimensions
Learning objectives (10)
LO-1Apply the scalar product to vectors expressed in Cartesian form.LO-2Determine a vector between two points.LO-3Examine and use addition and subtraction of vectors in Cartesian form.LO-4Examine properties of parallel and perpendicular vectors and determine if two vectors are parallel or perpendicular.LO-5Model and solve problems that involve displacement, force, velocity and relative velocity using the above concepts.LO-6Use a vector representing a section of a line segment, including the midpoint of a line segment.LO-7Use multiplication by a scalar of a vector in Cartesian form.LO-8Use scalar and vector projections of vectors. scalar projection of 𝒂 on 𝒃: |𝒂| cos(𝜃) = 𝒂 ⋅ 𝒃̂ vector projection of 𝒂 on 𝒃: |𝒂| cos(𝜃) 𝒃̂ = (𝒂 ⋅ 𝒃̂)𝒃̂ = (𝒂⋅𝒃 𝒃⋅𝒃) 𝒃LO-9Use the scalar (dot) product. 𝒂 ⋅ 𝒃 = |𝒂||𝒃| cos(𝜃) ( 𝑎1 𝑎2 𝑎3) ⋅ ( 𝑏1 𝑏2 𝑏3) = 𝑎1 𝑏1 + 𝑎2 𝑏2 + 𝑎3 𝑏3LO-10Use vectors to prove geometric results in two dimensions (other than those listed in Unit 2 Topic 3) and in three dimensions. Specialist Mathematics 2025 v1.4
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