Question

Rectangular components of vectors: The quantities Ax and Ay are called x, and y components of the vector A. Note that Ax is itself not a vector, but Axi is a vector, and so is Ayj. Using simple trigonometry, we can express Ax and Ay in terms of the magnitude of A and the angle θ it makes with the x-axis: Ax = A cosθ......(1) Ay = A sinθ.....(2) As is clear from above, a component of a vector can be positive, negative or zero depending on the value of θ. Now, we have two ways to specify a vector A in a plane. It can be specified by: (i) its magnitude A and the direction θ it makes with the x-axis; or (ii) its components Ax and Ay If A and θ are given, Ax and Ay can be obtained using Eq. (1)and (2). If Ax and Ay are given, A and θ can be obtained as follows: A = √(Ax2 + Ay2) And tan θ = Ay/Ax