MATH-M 311 Lecture Notes - Lecture 6: Dot Product, If And Only If, Cross Product
Document Summary
Section 12. 5 notes- equations of lines and planes in. Note: vectors often written vertically for convenience. Lines in 3-space- described by graphs of certain type of vec-val function: through origin- set of all scalar multiples of some fixed vector. If you pick a point, any other point on line is scalar multiple of. Points in direction of ; all lines through origin are of this form: not through origin. Any point can be obtained by scalar multiples of. Distance between 2 vectors = magnitude of difference: Shifting up one unit in direction gives function. Same thing as: can simplify vec-val functions as above into form. Inconsistent solutions for , so no solution; point does not lie on line: ex. Let distance2 from to distance between 2 vectors. Find value when is minimized, plug into when (known to be minimum because is upward-facing parabola is closest point. Equations of lines: can be found by:
