Math 1300 Assignment 2 Winter 2016 - MATH 1300 D01/D02...

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MATH 1300 D01/D02 Winter 2016 Assignment 2 SHOW ALL WORK to get full marks. Leave answers as exact answers. For example, leave it as fractions such as 1 { 7 as opposed to decimals such as 0 . 142857 . Word problems should have sentence answers with units. Fractions should be lowest terms. 1. [5] Determine an equation of the plane through the points P p 1 , ´ 1 , 3 q , Q p 2 , ´ 1 , 0 q and R p 3 , 1 , ´ 2 q . Your answer should be in standard form. 2. [5] Determine an equation of the line through the points P p 1 , ´ 3 , 2 q and Q p 6 , 2 , ´ 1 q in: (a) parametric form. (b) symmetric form. 3. For the lines x 5 t, y 2 ´ 3 t, z 3 ´ 2 t and 2 x ´ 3 10 y ´ 1 ´ 3 4 ´ z 2 : (a) [2] Show that the lines are parallel. (b) [5] Calculate the distance between the parallel lines. 4. For the lines x 1 “ p 1 , 2 , ´ 3 q ` s p 1 , ´ 2 , 0 q and x 2 “ p 1 , ´ 3 , 1 q ` t p 1 , 5 , 3 q : (a) [5] Show that the lines are skew. (b) [4] Calculate the cosine of the angle between the skew lines. (c) [5] Calculate the distance between the skew lines. 5. (a) [6] Determine the two planes parallel to the plane 2

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