Topic: Vectors

Generalize the analytical method of resolving and adding two vectors to three dimensions.

You may refer to the slides below:

I Adding vectors geometrically is .v not useful for vectors with 3 or '* " x more dimensions In Use analytical method: resolving A the vectors into components w! a m I respect to a coordinate system. M W I Drop perpendiculars from tip of a From gure, components of a, a to x and y-axes produces scalar can be obtained from its magni- components, or and a}. tude a and direction 6: or : n: cos :9 b1- : 39 cos 6' o Same with vector b: bx, by ' at. : a: sin 6' by = b sin 9 Vectors and Scalars Addition of Vectors, Geometric Method Resolution and Addition of Vectors, Analytic Method Examples Multiplication of Vectors Vectors and the Laws of Physics Resolution into scalar components (b) . Depending on 0, components of a vector may be positive or nega- tive . For a, A value makes it terminate h in the first quadrant b + ax >0, ay 20 O (a) (b) . Given a vector's components, one . For b, 0 value makes it terminate can obtain its magnitude and di- in the fourth quadrant rection thus: a = = bx >0, b,