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Topic 3: Vectors in the plane

Representing vectors in the plane by directed line segments

5 hours

• Examine examples of vectors including displacement, velocity and force.
• Understand the difference between a scalar and a vector including distance and displacement, speed and velocity, and magnitude of force and force. 1 interactive
• Define and use the magnitude and direction of a vector. 1 interactive
• Understand and use vector notation: AB⃗, ã, and unit vector notation â.
• Understand and use vector equality.
• Represent and use a scalar multiple of a vector. 1 interactive
• Use the triangle rule to represent the resultant vector from the sum and difference of two vectors. 1 interactive
• Represent a vector in the plane using a combination of the sum, difference and scalar multiple of other vectors.

Vectors in two dimensions

5 hours

• Use ordered pair notation (x, y) and column vector notation to represent a position vector in two dimensions.
• Calculate the magnitude and direction of a vector.
• Calculate and use a unit vector, â, in the plane.
• Define and use unit vectors and the perpendicular unit vectors î and ĵ.
• Express a vector in Cartesian (component) form using the unit vectors î and ĵ.
• Understand and express a vector in the plane in polar form using the notation (r, θ).
• Convert between Cartesian form and polar form, with and without technology.
• Understand and use the Cartesian form and polar form of a vector.