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MATH1151 week4c3 - Week 4 Friday 11-12 Class Time allowed...

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Time allowed: 15 minutes. 1. (2 marks) Let A = 6 1 0 , B = 3 2 6 (a) Find in parametric vector form the equation of the line through A and B . (b) Find the coordinates of the point C such that B lies on the interval AC and | AB | = 1 4 | AC | . 2. (2 marks) Let A and B be points with position vectors ˜ a and ˜ b respectively. Let M be the mid-point of AB , and suppose that N has position vector 3( ˜ a + ˜ b ). Write down the position vector of M , and prove that O , M and N are collinear. 3. (3 marks) Prove that A = 0 4 3 , B = 5 7 2 , C = 1 3 5 , D = 4 0 4 are the vertices of a parallelogram. Draw and label the parallelogram. 4. (3 marks) For the following system of equations, write down the corresponding augmented matrix, use Gaussian elimi- nation to transform the augmented matrix into row-echelon form, and solve the system of equations, writing your answer in vector form.
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