Dot Product of Two Vectors ac+bd

Example 1

Example 2 u= v=w=

Angle Between Two Vectors

Example 3 Find the angle between the two vectors

Use the formula to determine the the angle between two vectors whose dot product is zero.

~Flashback~ A=30ºa=12 B=45ºb= C=c= This is an oblique triangle with what given information? What do you use to solve for the sides? What is angle C and sides b & c ?

6.4 Finding Vector Components & Work

Added Two vectors

Find the projection of u= onto v=. Write u as the sum of two orthogonal vectors, one of which is proj v u

1500 lb. boat at a 20 degree incline.

200 lb. cart on a 30 degree incline.

Work

A force of 45 lbs. in the direction of 30 degrees above the horizontal is required to slide a table across the floor. Find the work done if the table is dragged 20 feet.

50 lb. force, 12 ft. wide door

58) A force of 45 pounds in the direction of 30 degrees above the horizontal is required to slide a table across a floor. Find the work done if the table is dragged 20 feet.

59) A toy wagon is pulled by exerting a force of 20 pounds on a handle that makes a 25 degree angle with the horizontal. Find the work done in pulling the wagon 20 feet.

60) A mover exerts a horizontal force of 25 pounds on a crate as it is pushed up a ramp that is 12 feet long and inclined at an angle of 20 degrees above the horizontal. Find the work done on the crate.