Topic: Vectors

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

You may refer to the slides below:

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 . Adding vectors geometrically is not useful for vectors with 3 or more dimensions . Use analytical method: resolving b the vectors into components w/ respect to a coordinate system. (a) (b) . Drop perpendiculars from tip of . From figure, components of a, a to x- and y-axes produces scalar can be obtained from its magni- components, ax and dy tude a and direction 0: . Same with vector b: br, by ax = acos 0 bx = bcos 0 ay = asine by = b sineVectors 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, 0 value makes it terminate in the first quadrant ax >0, ay >0 (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 = 1 = bx >0, by