Honors Pre-Calculus 12-4 The Dot Product Page: 441 Objective: To define and apply the dot product

then the dot product of the vectors is defined by:

If v = (-2,5) and w = (4, 1), find a) v۰wb) v ۰ v

Theorem Properties of Dot Product If u, v, and w are vectors, then k(uv) = (ku) v

Theorem Angle between Vectors

Find the angle θ between u = (2, -1) and v = (4, 3)

Two vectors v and w are said to be parallel if there is a nonzero scalar  so that v =  w. In this case, the angle  between v and w is 0 or 

The vectors are parallel since w = 3v. Determine whether the vectors v = (-3, 2) and w = (-9, 6) are parallel.

Theorem Two vectors u and v are orthogonal if and only if

Determine whether the vectors v = (4, -1) and w = (2, 8) are orthogonal.

Theorem

The work W done by a constant force F in moving an object from A to B is defined as

Find the work done by a force of 50 pounds acting in the direction 3i + j in moving an object 20 feet from (0, 0) to (20, 0).

(3, 1) (20, 0) ||F|| = 50

Work is approximately foot-pounds.

TB p. 444 #3, odd, 25