Pre-Calc 8.4 Dot Product & Cross Product PDF

Pre­Calc 8.4.notebook December 07, 2017 8.3­ Dot Product and Cross Product of Vectors Objective: Be able to find the dot product and cross product of 2 vectors. Dot Product(also known as...

Pre­Calc 8.4.notebook December 07, 2017 8.3­ Dot Product and Cross Product of Vectors Objective: Be able to find the dot product and cross product of 2 vectors. Dot Product(also known as Inner product) 1 Pre­Calc 8.4.notebook December 07, 2017 Another property of dot product is finding the angle between the vectors. cos Θ= a b |a| |b| Example: a = (6,2), b= (­4,3) Example­ u = (6,­5,1), v = (­8,­9,5) 2 Pre­Calc 8.4.notebook December 07, 2017 work­ magnitude of a force applied to an object times by the distance through which an object moves parallel to the applied force. Work measured in joules. Formula: W = |F| cos Θ |AB| Example­ a person pushes a car with a constant force of 120 Newtons at a constant angle of 45 degrees. Find the work done in joules moving the car 10 feet. W = 120 cos 45 10= 848.5 joules Rick is pushing a vacuum cleaner with a force of 65 lbs. The handle of the vacuum makes a 60 degree angle with the ground. How much work in foot­pounds does he do if he pushes the vacuum cleaner 6 feet. w = 65 cos 60 6 = 195 foot­pound 3 Pre­Calc 8.4.notebook December 07, 2017 | Cross Product only done in 3 space!!! V=(v1, v2,v3) W= (w1,w2,w3) If cross product = (0,0,0), then the original vectors are parallel!! The cross product is Perpendicular to each of the original vectors! 4