Vectors in three dimensions
Specialist Mathematics · Unit 3 — Further complex numbers, proof, vectors and matrices · Vectors in two and three dimensions
Learning objectives (7)
LO-1Calculate and use a unit vector, 𝒏̂, in three-dimensional space. 𝒏̂ = 𝒏 |𝒏|LO-2Calculate the magnitude of a vector |𝒂| = |( 𝑎1 𝑎2 𝑎3)| = √𝑎12 + 𝑎22 + 𝑎32LO-3Define and use the altitude angle 𝜑.LO-4Define and use unit vectors and the perpendicular unit vectors 𝒊̂, 𝒋̂ and 𝒌̂.LO-5Express a vector in Cartesian (component) form using the unit vectors 𝒊̂, 𝒋̂ and 𝒌̂.LO-6Use Cartesian coordinates for three-dimensional space, including plotting points.LO-7Use ordered triple notation (𝑥, 𝑦, 𝑧) and column vector notation ( 𝑥 𝑦 𝑧) to represent a position vector in three dimensions.
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