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prelim1

# prelim1 - Math 192 Prelim 1 7:30-9:00 You are NOT allowed...

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Math 192, Prelim 1 September 27, 2007. 7:30-9:00 You are NOT allowed calculators, the text, or any other book or notes. SHOW ALL WORK! Write your name and Lecture/Section number on each booklet you use 1) The position vector of a moving particle is given by r ( t ) = (1 + t ) i + ( t 2 - 1) j + 2 t k . a) (6 points) Find the velocity and acceleration vectors. b) (6 points) Find, as a function of t , the cosine of the angle between the velocity and acceleration vectors. 2) Consider the planes P 1 and P 2 given respectively by x + 2 y + 3 z - 1 = 0 and x - 2 y = 0. a) (8 points) Find the point of intersection of P 2 with the line passing through A (1 , 1 , 1) and B (2 , 0 , 0). b) (8 points) Find a parametric equation of the line in which the planes P 1 and P 2 intersect. 3) Consider the three points A, B and C with coordinates (1 , 0 , 2), ( - 2 , 1 , - 1) and (1 , 1 , 1). a) (8 points) Find the area of the triangle ABC . b) (8 points) Find the distance from
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