Mth211 Fundamentals of Mathematical Methods and Mechanics

MTH211fundamentals of mathematical methods and mechanics

In this question, you are to apply vectors and vector algebra. Note that throughout this question vectors are shown in bold type. In your solution to all questions involving vectors, you should use underlining to show a vector quantity. Failure to do so will lose marks.

(a) The points A, B and C have coordinates (-4, 0), (-3, 4) and (2, -2) respectively, with respect to a two-dimensional Cartesian coordinate system with origin O.

(i) Draw a diagram showing A, B and C.

(2 marks)

(ii) Determine the polar representation of the point B.

(iii) Write the position vectors of A, B and C in terms of Cartesian unit vectors i

and j.

(iv) Find a unit vector in the direction of C.

The points P, Q and R have coordinates (2, -3, 4), (-1, -2, -1) and (-3, 4, 5) respectively, with respect to a three-dimensional Cartesian coordinate system with origin O. The vectors OP,OQ and OR are denoted by p, q and r respectively. In this part of the question you should express all vectors in the form a1i + a2j + a3k, where i, j and k are Cartesian unit