Vectors and scalars

Understand that vectors are quantities that have both magnitude and direction, while scalars are quantities with only magnitude.
Grasp that vectors can be represented visually by arrows, where the length of the arrow represents the vector’s magnitude and the direction of the arrow represents its direction.
Examples of vectors include displacement, velocity, acceleration, and force.
Know that scalars include distance, speed, mass, time and energy.

Addition and Subtraction of Vectors

Grasp how to add vectors graphically by placing them head to tail and drawing the resultant from the tail of the first vector to the head of the last vector.
Understand that subtracting a vector is the same as adding its inverse.
Recognise that vectors can also be added and subtracted analytically by breaking them down into their components.
Learn that the components of a vector are its projections in the coordinate directions.

Scalar Multiplication of Vectors

Recognise that when a vector is multiplied by a scalar, its magnitude is multiplied by the absolute value of the scalar and its direction is reversed if the scalar is negative.

Dot and Cross Products

Know that the dot product of two vectors is a scalar and represents the product of the two vectors’ magnitudes and the cosine of the angle between them.
Grasp that the cross product of two vectors is a vector. Its magnitude is equal to the product of the two vectors’ magnitudes and the sine of the angle between them and its direction is perpendicular to the plane containing the two vectors.

Resolving Vectors

Understand how to resolve vectors into their components using trigonometric functions.
Practice resolving vectors in two dimensions using sine and cosine to determine the components.
Learn to work in any chosen coordinate system, normally the system best suited to the physical problem at hand is chosen.

Vector Applications

Be able to apply vector addition and subtraction in understanding the superposition of forces.
Grasp the concepts of balanced and unbalanced forces and how they relate to vector quantities.
Appreciate the role of vectors in physical principles such as Newton’s Laws.

Remember that practicing problems is the most effective way to solidify your understanding of vectors and their applications. Aim to not only be able to perform the calculations, but also to have a clear conceptual understanding of what vectors represent.