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HOMEWORK PROBLEMS Week 1: Due Friday 18 January 1. A straight line AB is drawn between the two points A(5, 2, 8) and B(3, 5, 0) in Cartesian...

HOMEWORK PROBLEMS Week 1: Due Friday 18 January 1. A straight line AB is drawn between the two points A ( 5 , - 2 , 8 ) and B ( - 3 , 5 , 0 ) in Cartesian coordinates Oxyz , where the coordinates are measured in meters. (i) Find the length of the line AB . (ii) Express the relative position vector r AB as a Cartesian vector. (iii) Find the Cartesian form of the unit vector in the direction AB . (iv) Find the angle between the line AB and the positive x - axis. (v) A force of 200 N acts along the line AB . What is its component in the positive z - direction? 2. In Figure 2, ADB is a straight line and the length AD = 3 m. Find a Cartesian position vector deﬁning the point D and hence ﬁnd the Cartesian description of the unit vector e CD deﬁning the direction of the line CD . A B x y z C D 4 3 4 5 1.5 all dimensions in meters Figure 2 1
3. The hinged plate in Figure 3 is supported by the cord AB . If the tension in the cord is 340 lb, express the force F that it exerts on the plate as a Cartesian vector. Also, ﬁnd the length of the cord. A B x y z 8 9 6 all dimensions in feet Figure 3 2
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