Dot Product of Vectors.

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Presentation transcript:

Dot Product of Vectors

Definition of Dot Product Given: Two vectors in Component form

Example: Find the Dot Product

Dot PRODUCT The result is not a vector. It is a real number, that is, a scalar. For this reason, the dot product is sometimes called the scalar product (or inner product).

Properties of the Dot Product Let u, v, and w be vectors in the plane or in space and let c be a scalar.

DOT PRODUCT— Alternative-DEFINITION If is the angle between the vectors a and b, then

If is the angle between the nonzero vectors a and b, then

Example:

Orthogonal Vectors Perpendicular orthogonal What will be the dot product of two orthogonal vectors?

A use of the dot product is found in the formula below: The work W done by a constant force F in moving an object from A to B is defined as This means the force is in some direction given by the vector F but the line of motion of the object is along a vector from A to B

Class-work

Home work Page-586+ Quick review exercise 1-5, 7, 10 Section 12.2 exercise 7, 36 14 (optional)