MAT 21C Lecture Notes - Lecture 13: Vector Projection, Scalar Multiplication, Cross Product
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MAT 21C Full Course Notes
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Announcements: hw5 due 10/26, o ce hours m 10/24 3-4 msb3106 f 10/28 1-2 msb 3106. Let ~u = hu1, u2, u3i and ~v = hv1, v2, v3i be two vectors and k a scalar. Addition: ~u + ~v = hu1 + v1, u2 + v2, u3 + v3i. Scalar multiplication: s ~u = hsu1, su2, su3i. Dot product: ~u ~v = u1v1 + u2v2 + u3v3. Cross product: ~u ~v = h i. Vectors ~u and ~v are orthogonal if ~u ~v = 0. Rule (the angle between two non-zero vectors ~u and ~v ). cos = Rule (the vector projection of ~u onto ~v ). proj ~v ~u = (| ~u | cos ) | ~v |2 (cid:19) ~v example: pulling a box with force ~u is moving the box in direction ~v . Rule (the scalar component of ~u in the direction of ~v ). The cross product ~u ~v is the vector.
