Specialist Mathematics ยท Unit 3 ยท Vectors in two and three dimensions ยท Algebra of vectors in three dimensions
Use the scalar (dot) product. ๐ โ ๐ = |๐||๐| cos(๐) ( ๐1 ๐2 ๐3) โ ( ๐1 ๐2 ๐3) = ๐1 ๐1 + ๐2 ๐2 + ๐3 ๐3
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Use scalar and vector projections of vectors. scalar projection of ๐ on ๐: |๐| cos(๐) = ๐ โ
๐ฬ vector projection of ๐ on ๐: |๐| cos(๐) ๐ฬ = (๐ โ
๐ฬ)๐ฬ = (๐โ
๐ ๐โ
๐) ๐
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Use 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