Lesson Objective Understand what vectors are and the notation Begin to use the notation to solve geometry problems.

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Presentation transcript:

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 DiagramColumn vectorUnit Vector 12i – 5j 30 o

Vector arithmetic: Adding SubtractingMult/Divi by a scalar

Consider the two vectors shown: Write each of the vectors below in terms of a and b ab cde f g h i j k l m n 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 135 o. 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