# 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.  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.  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)  Show that the lines are parallel. (b)  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)  Show that the lines are skew. (b)  Calculate the cosine of the angle between the skew lines. (c)  Calculate the distance between the skew lines. 5. (a)  Determine the two planes parallel to the plane 2
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