PILOT Problem Set 1.pdf - Calculus III PILOT Problem set 1 1 The center of mass of triangle ABC is the point G defined by ~ GB ~ GC ~ =0 GA Show that

# PILOT Problem Set 1.pdf - Calculus III PILOT Problem set 1...

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Calculus III PILOT Problem set 1 1. The center of mass of triangle ABC is the point G defined by ~ GA + ~ GB + ~ GC = 0 . Show that for any choice of origin O, ~ OG = ~ OA + ~ OB + ~ OC 3 . 2. Show that the point G in problem 1 is the centroid of triangle ABC, that is, the intersection of all the medians of the triangle. Hint: Take O=A. 3. Find the distance from the point (3,2) to the line x + y = - 2 using vector methods. Unformatted text preview: 4. Find a unit vector orthogonal to the line ~ X ( t ) = (-1 ,-1 , 2) + t (2 ,-1 , 1) and the vector ˆ i-ˆ j . 5. Find the equation of the plane that contains (3,-1,2) and the line ~ X ( t ) = (2 ,-1 , 0) + t (2 , 3 , 0) . 6. Find the line through (3,1,-2) that intersects and is perpendicular to the line x =-1 + t, y =-2 + t, z =-1 + t . 1...
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• Fall '10
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