126_Au07_Sol1 - Math 126, Sections C and D, Fall 2007,...

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Unformatted text preview: Math 126, Sections C and D, Fall 2007, Solutions to Midterm I 1. For the questions below use the points P (2 , 1 , 5), Q (- 1 , 3 , 4) and R (3 , , 6). (a) Find a vector orthogonal (perpendicular) to the plane through the points P , Q and R . vector PQ vector PR = vextendsingle vextendsingle vextendsingle vextendsingle vextendsingle vector i vector j vector k- 3 2- 1 1- 1 1 vextendsingle vextendsingle vextendsingle vextendsingle vextendsingle = vector i + 2 vector j + vector k (b) Find the area of the triangle PQR . The area is 1 2 the length of the vector you found in part (a). Area = 1 2 vextendsingle vextendsingle vector i + 2 vector j + vector k vextendsingle vextendsingle = 1 2 1 + 4 + 1 = 6 2 (c) Determine if the point T (0 , 3 , 3) is on the same plane as P , Q and R . You need to check that vector PT (or vector QT or vector RT ) is perpendicular to the vector you got in part (a) using the dot product. vector PT ( vector i + 2 vector j + vector k ) = (- 2 vector i + 2 vector j- 2 vector k ) ( vector i + 2 vector j + vector k ) = 0 So it is....
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126_Au07_Sol1 - Math 126, Sections C and D, Fall 2007,...

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