guideF09 - MATH 210 Sample exam problems for the 1st hour...

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MATH 210 Sample exam problems for the 1st hour exam Fall 2009 1. Let A = (1 , 1 , 2) , B = (0 , 1 , 1) , C = (2 , 1 , 1). (a) Find the vector equation of the plane through A,B,C . (b) Find the area of the triangle with these three vertices. 2. Find the vector of length one in the direction of −→ v −→ u where −→ v = ( 7 , 5 , 3 ) and −→ u = ( 4 , 5 , 7 ) . 3. Let −→ r ( t ) = (big 3 t 1 ,e t , cos( t ) )big . (a) Find the unit tangent vector −→ T to the path −→ r ( t ) at t = 0. (b) Find the speed, vextendsingle vextendsingle vextendsingle vextendsingle −→ r ( t ) vextendsingle vextendsingle vextendsingle vextendsingle at t = 0. 4. Given a point P = (0 , 1 , 2) and the vectors −→ u = ( 1 , 0 , 1 ) and −→ v = ( 2 , 3 , 0 ) , find (a) an equation for the plane that contains P and whose normal vector is perpendicular to the two vectors −→ u and −→ v , (b) a set of parametric equations of the line through P and in the direction of −→ v . 5. Find the speed and arclength of the path −→ r ( t ) = ( 3 cos t, 4 cos
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