(Vectors and Scalars)
A vector that lies in the x–y plane is described by its magnitude A and by the angle θ it makes with the positive x–axis.
Answer the following questions in sequence.
(a) Define a unit vector and explain its significance when representing a vector in component form.
(b) Starting from the right–angled triangle formed by the components of the vector, derive expressions for Ax and Ay in terms of A and θ.
(c) Using the results of part (b), prove that A=Ax2+Ay2 and that tanθ=AxAy.
(d) Briefly describe how the idea of components is extended when the vector has a non-zero z-component. State the role of the unit vectors i^,j^,k^ in such a case.