ENGEN183 B 6-09-2018 - Lecture notes 41 PDF

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The lecturers were Nicholas Cavenagh and Steven Miller...

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DSS Notes Paper: ENGEN183B Date: 06/09/2018 Lecture 26 The Cross-Product Recall dot product:

The dot product is a scalar. Exercise: If u = (2, -1, 2) and v = (4, -1, -4) then compute u x v Solution:

Exercise: If u = (0, 1, 7) and v = (13, -5, 3) then compute u x v Solution:

Cross production only exists in 3 or 7 dimensions !!! Properties: • u x v = -v x u ◦ Q. Why does u x v = -v x u ? uxv=

• (hence) u x u = 0 If v = u then u x u = -u x u Hence, u x u = 0 = (0, 0, 0) Scalar triple product Scalar triple product u (v x w) = (u x v) w Exercise: Show that u x v is orthogonal to both u and v. Solution: u (u x v) = (u x u) v =0 v =0 u is orthogonal to u x v v (u x v) = v (-v x u) by (1) = - (v (v x u)) = - ((v x v) u) = - (0 u) = -0 = 0 v is orthogonal to u x v...