Section 3.3 – The Cross Product Unit 3 – Vectors Section 3.3 – The Cross Product Calculator Required

Vocabulary First (Again  ) Determinant – a number (scalar) Notations The 2 x 2 Determinant

Try these four… …and these four

The MINOR of a matrix Cross out the row and column of the element Compute the determinant of what remains

The 3 x 3 Determinant 1. Select ANY row or column (most zeros would be smart) 2. Take each element and multiply it by its MINOR. Apply + - + - + - (to be explained). Remember the + starts with the first row first column element. + – +

+ – + – + – – + –

– + – + – + = 0

Definition The cross product of two vector yields a vector which Is orthogonal to the two given vectors. If A = ai + bj + ck and B = di + ej + fk

Find the vector orthogonal to A = 2i + 3j + k and B = 3i - 2j + 5k

Find the vector orthogonal to A = 7i + 1j + 2k and B = i + 3j + 4k