Understanding The Scalar Product

Comprehending the scalar product (or dot product) as a method of multiplying two vectors together to get a scalar.
Recognising that the scalar product of two perpendicular vectors is zero.
Demonstrating knowledge of the angle formula for the scalar product and being able to use it to calculate the angle between two vectors.

Calculating The Scalar Product

Understanding how to carry out the computation of the scalar product of two vectors in component form, knowing that the scalar product of vectors a = (a1, a2) and b = (b1, b2) is given by a.b = a1b1 + a2b2.
Being able to calculate the scalar product of two vectors given their components or their magnitudes and the angle between them.
Correctly applying the distributive law of the scalar product, i.e., for any vectors a, b, and c, and any scalar k, a.(b+c)=a.b+a.c, and (ka).b = k(a.b).

Utilising the scalar product to find the angle between two vectors and understanding that this method gives the smaller of the two possible angles (resolving ambiguities by considering the context of the problem).
Applying the scalar product to determine if two vectors are perpendicular, that is, if their scalar product is zero.
Employing the scalar product in problem solving involving vectors, such as checking whether given points lie on a straight line (collinearity), or determining the relative positioning of points in the plane or space.