Grade 11 Mathematics Unit 5 : Vectors

This unit introduces you to vectors, which are mathematical objects that possess both magnitude (length) and direction. You’ll learn how to represent vectors, perform operations on them, and apply them to solve problems in geometry, physics, and other fields.

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Chapter 5.1 – Revision on Vectors and Scalars

This chapter revisits the fundamental ideas that separate vectors from regular numbers.

• Distinguish between scalars (quantities with only magnitude, like speed or temperature) and vectors (quantities with both magnitude and direction, like velocity or force).
• Review basic graphical operations like vector addition using the Triangle or Parallelogram Laws and scalar multiplication.

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Chapter 5.2 – Representation of Vectors

Learn how to work with vectors algebraically in a coordinate system.

• Represent vectors in component form or in terms of standard unit vectors.
• Calculate the magnitude (length) of a vector using the distance formula.
• Find the unit vector, which has a magnitude of 1 but points in the same direction as the original vector.

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Chapter 5.3 – Vector Product

Discover the two distinct ways to multiply vectors, each yielding a different type of result.

• Scalar (Dot) Product: Learn how to calculate the dot product, which results in a single number (a scalar). This product is useful for finding angles between vectors.
• Vector (Cross) Product: Understand the cross product, which is performed on 3D vectors and results in a new vector that is perpendicular to both of the original vectors. .

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Chapter 5.4, 5.5 & 5.6 – Applications

Apply the dot and cross products to solve meaningful problems in mathematics and physics.

• Use the dot product to:
  • Find the angle between two vectors.
  • Determine if two vectors are orthogonal (perpendicular).
  • Calculate the work done by a force.
• Use the cross product to:
  • Find a vector perpendicular to two given vectors.
  • Calculate the area of a parallelogram or triangle in space.
  • Calculate torque in physics.

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Learning Outcomes

By the end of this unit, you’ll be able to:

• Understand the basic concepts of vectors and perform operations on them.
• Apply theorems about vectors, such as the dot and cross product, to solve problems.
• Solve real-world problems involving forces, work, and geometry using vector principles.