SJSU EE 140 - ch2_Vector_Algebra (16 pages)

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Chapter 2 Vector Algebra Review Dr Ray Kwok SJSU Vector Algebra Dr Ray Kwok Vector products scalar scalar scalar scalar a b ab e g 2 4 kg 8 kg scalar vector vector e g 5 2 x 4 y 10 x 20 y r r k A kA vector times vector r r can be scalar scalar product or dot product A B or r r vector vector product or cross product A B Can you add a vector to a scalar Vector Algebra Dr Ray Kwok The scalar product dot product r r A B AB cos x x 1 y y z z x y 0 x z y z r r A B A x x A y y A z z Bx x B y y Bz z r r A B A x B x A y B y A z Bz e g r A 2x 2 y r B 3x y What is A B e g What s the angle between these 2 arrows Vector Algebra Dr Ray Kwok Interpretation projection Vector Algebra Dr Ray Kwok Example Work r r W F x Projection So is the uplifting force doing anything at all Vector Algebra Dr Ray Kwok The vector product cross product r r A B AB sin x x 0 y y z z x y z right hand coordinate y z x cyclic permutation z x y y x z z y x x z y e g r A 2x 2 y r B 3x y What is A x B x r r A B Ax y z Ay Az Bx By Bz e g What s the angle between these 2 arrows Vector Algebra Dr Ray Kwok Example calculate torque r r r F r 4N x o 40o 1 5 m choose counter clockwise o 1 5 4 sin 40o 3 86 N m counter clockwise Vector Algebra Dr Ray Kwok Example perpendicular F 4N 40o x 1 5 m o 4 sin 40o 1 5 m x o o 1 5 4 sin 40o 3 86 N m counter clockwise Vector Algebra Dr Ray Kwok Example moment arm 4N 40o x 1m o 1 5 m 1 5 sin 40o o 40 x o 4N 1 5 m o 4 1 5 sin 40o 3 86 N m counter clockwise Vector Algebra Dr Ray Kwok Exercise 1 Find a b c d e f r r A B r r B 2A r r A B r r A B r r A A r r B B r A x 4 z r B 2 x y z g Angle between A and B h Find a vector that is perpendicular to A and B Vector Algebra Dr Ray Kwok Triple vector product scalar vector Ax r r r A B C Bx Cx Ay Az By Cy Bz Cz r r r r r r r r r r r r