8.5 The Dot Product.

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Presentation transcript:

8.5 The Dot Product

Theorem Properties of Dot Product If u, v, and w are vectors, then Commutative Property Distributive Property

Theorem Angle between Vectors

v = 4i + 3j v = 2i - j

Two vectors v and w are said to be parallel if there is a nonzero scalar a so that v = aw. In this case, the angle q between v and w is 0 or p.

Determine whether the vectors v = -3i + 2j and w = -9i + 6j are parallel. The vectors are parallel since w = 3v.

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

Determine whether the vectors v = 4i - j and w = 2i + 8j are orthogonal.

y w = 2i + 8j x v = 4i - j

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).

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

Work is approximately 948.68 foot-pounds.

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