By A. V. Durrant (auth.)
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Extra resources for Vectors in Physics and Engineering
2 (Objective 3) (a) Show that if a particle is held in equilibrium under the action of three noncollinear and non-zero forces then the forces must be coplanar. (b) Is the statement in part (a) also true for four forces? 2 N and the tension force T of the string. Determine the magnitude and the direction of T. 47 The pendulum bob is held in equilibrium by three forces. 48 given that the four forces are in equilibrium. S (Objectives 3,4) ABeD is a square. Forces of magnitudes 1 N, 2 N and 3 N act parallel to AD, BC and CD respectively.
Therefore t 1 1 OM = -[(3,-5,7) + (3,-4,2)] = -(6,-9,9). l. (a) Express u, v and w explicitly in terms of the cartesian unit vectors. (b) Write down the vector q = u - w - k in terms of the cartesian unit vectors. (c) Evaluate Iq I and write down the unit vector (d) What is the angle between the unit vector k? q q. 2 (Objectives 7,8,10,11) Given two vectors r = 3i + 2j - k, s = -2i + 5j + 7k (a) Determine r + s, r - s and r + j + k, and give your answers as ordered triples. 36 Vector algebra 1: Scaling and adding vectors (b) Determine rx> sz' (r - s)y and 1r + S I.
6°. It is necessary to decide whether R is directed above or below the x-axis. We note that Ry = 417 which is positive. 6°. 46 The position of charge q relative to charge Q is given by the displacement r - R. IqQI 41tE od where 41tEo is a scalar constant (Appendix A). The direction of F is along the line joining the charges and is directed away from Q (repulsive) when the charges have the same sign (like charges) and towards Q (attractive) when they have opposite signs (unlike charges). Express the force vector F in terms of the position vectors r of q and R of Q.