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- A particle with position vector r= 5i−3j−k(m) has a force f=−2i+j+ 9k(N) acting on it. Determine the magnitude (to 1 decimal place) of the torque about the origin.
2.Three pulling forcesF1,F2andF3are acting on a particle,p, as indicated in the diagram below (notto scale) whereθ1= 45◦andθ2=θ3= 30◦. If||F1||= 10 and the particle is at rest, determine the magnitude of vectorsF2 and F3 to two decimal places.
3.Find the point of intersection and the acute angle (in degrees and radians, to 1 decimal place) betweenthe lines described by the vector.
4.A plane is flying at a constant altitude on a heading of N52◦E with a speed of 740 km h−1. Wind is blowing from the South East at a 37 km h−1.
a) Find the magnitude of the resultant velocity of the plane to the nearest integer.
b) How many degrees off course does the plane end up because of the wind? Give your answer to 2decimal places.
5.a) Show thatzw=zw.b) Considerz= 4 + 2iandw= 7−i. Determine|(z+w)(z−w)|.(4 marks)6.Find the exact value of cis(π12)in the forma+biwherea,b∈R. Hence, use this result to determinethe exact value of tan(π12).
