Transcript Slide 1
Lesson Objective Understand what vectors are and the notation Begin to use the notation to solve geometry problems Ways to represent vectors: Represent each vector as a diagram, a column vector and using unit vectors Diagram Column vector Unit Vector 4 0 2 3 12i – 5j 30o Vector arithmetic: Adding Subtracting Mult/Divi by a scalar Consider the two vectors shown: a b Write each of the vectors below in terms of a and b f c d e i g h j k l n m o p Vector Geometry: Lesson Objective Be able to find the magnitude and direction of a vector written in component form and be able to break a vector into components Begin to use components to solve problems connected with velocity and force Magnitude, or size of a Vector in 2d and 3d: Consider a particle moving with velocity u = 3i – 4j What is its actual speed? What is its actual direction? What if the particle had a velocity of u = 3i -4j + 12k? 1) Consider the force, P = 2i + 3j and Q = 4i – 7j acting on a point mass. What is the resultant force on the mass? What is the magnitude of this force and in what direction is it acting? 2) A small boy aims to swim directly (due north) across a river that flows east-west with a speed of 2ms. The river is 10m wide. If he heads directly north, how far will he be swept down stream? What is his actual speed in ms-1 What direction should the boy head in to off-set the action of the current on him, so that he really does swim directly/due north across the river ? A small motor boat moving at 8 km/h relative to the water travels directly between two lighthouses which are 10 km apart, the bearing of the second lighthouse from the first being 135o. The current has a constant speed of 4 km/h from the east. Find: i) The course that the boat must set ii) The time for the journey In each question write down the value of component X 20N 60o X In each question write down the value of component X 12N 45o X In each question write down the value of component X 5N X 30o In each question write down the value of component X X 30o 8N In each question write down the value of component X X 30o 10N In each question write down the value of component X 8N 80o X In each question write down the value of component X 5N 20o X In each question write down the value of component X 7N X 18o In each question write down the value of component X X 70o 4N In each question write down the value of component X X 12N 15o In each question write down the value of component X X 50o 30N In each question write down the value of component X 8N 15o X In each question write down the value of component X 25N 40o X In each question write down the value of component X X 70o 12N In each question write down the value of component X 40N X 130o In each question write down the value of component X 150o 25N X