Vectors

Understanding Vectors

• Recognise the concept of a vector as a quantity having both magnitude and direction.
• Understand that two vectors are equal if they have the same magnitude and direction, regardless of their initial position.
• Distinguish between position vectors and displacement vectors.

Vector Arithmetic

• Perform basic vector operations, including vector addition, subtraction, and multiplication by a scalar.
• Appreciate that the sum of two vectors gives a resultant vector.

Scalar Product

• Grasp the idea of the scalar product and its representation in both the geometric and algebraic form.
• Deliver the concept that a scalar product of two vectors can be obtained by multiplying their magnitudes and the cosine of the angle between them.
• Understand how to find the angle between two vectors using the scalar product.

Vector Equations

• Learn to express the equation of a line in vector form.
• Solve vector equations and understand the importance of the parameter in the equation of a line.

Applications of Vectors

• Understand how to break down a vector into components in two and three dimensions.
• Utilise vectors to solve problems in geometry such as finding the area of a parallelogram or triangle.
• Apply vectors to real-world applications such as velocity and force.