Question

In (Multivariable Calculus > Part C: Parametric Equations for Curves > Session 17: General Parametric Equations; the Cycloid - Problems & solutions), can anyone please explain why vector OC has components 12t and 12t and not 12√2t and 12√2 t, as the direction vector in the direction of OC has components 1 & 1.

Answer 1

The unit vector in the direction of vector <1, 1> is the vector <\[1/\sqrt{2}, 1/\sqrt{2}\]> because the length of <1, 1> is \[\sqrt{2}\] so that the centre of the circle moves 12\[\sqrt{2}\] cm/sec times this unit vector.

Answer 2

Thanks