A student wishes to clarify the basic idea of components of a vector in a plane.
a. (i) Define a vector quantity and a unit vector, giving one example of each.
b. (ii) With the help of a neatly-labelled diagram, explain how a vector of magnitude V making an angle θ with the positive x-axis can be expressed in terms of its rectangular components Vx and Vy.
c. (iii) Explain, without carrying out a full algebraic derivation, why the magnitude of the original vector equals Vx2+Vy2. State the geometrical principle involved.