# A3 - a,b,c to c,a,b What is the smaller angle between ~v...

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MATH 222, Calculus 3, Fall 2011 Assignment 3, due in class Monday, October 3, 2011 1. Find the Maclaurin series ﬁrst for (1 - t 2 ) - 1 2 and then for arcsin x = sin - 1 x . (Hint: integrate.) Use this give another formula for π 4 . 2. Find a unit vector perpendicular to both h- 3 , 1 , 2 i and h 1 , 2 , 3 i . 3. Show that the points P ( - 2 , 1 , 3), Q (2 , 3 , 0) and R ( - 6 , - 1 , 6) are collinear. 4. Let ~v be a vector in 3-space such that the angle between ~v and ~ i is 2 π 3 , and the angle between ~v and ~ j is π 4 . There are two possible values for the angle between ~v and ~ k . What are they? 5. Suppose that a , b and c are distinct real numbers, ~v is the vector from ( a,b,c ) to ( b,c,a ) and ~w is the vector from (
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Unformatted text preview: a,b,c ) to ( c,a,b ). What is the smaller angle between ~v and ~w ? 6. Show that the lines deﬁned by ‘ : ( x,y,z ) = (0 , 2 , 4) + s h 7 , 1 ,-3 i and ‘ : ( x,y,z ) = (3 , 5 , 6) + t h-1 , , 2 i are skew. Find the shortest distance between these lines. 7. Find the point P which is the intersection of the lines ‘ : ( x,y,z ) = (3 , ,-3) + s h 2 ,-4 , 1 i and ‘ : ( x,y,z ) = (3 ,-25 , 4) + t h 10 , 5 ,-2 i . Give a parametric equation for the line connecting the origin to P. 1...
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