Test 1_MAT 2030_11SS

# Test 1_MAT 2030_11SS - (6 Find the cross product a × b and...

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Name : MAT 2030, Calculus III, Test 1 No calculators needed or allowed! Questions : (50 + 5 points) (1) Determine whether the points lie on straight line: A (2 , 4 , 2), B (3 , 7 , - 2), and C (1 , 3 , 3). [6 pts] (2) If v lies in the ﬁrst quadrant and makes an angle π/ 3 with the positive x -axis and | v | = 4, ﬁnd v in component form. [6 pts] (3) Find the unit vectors that are parallel to the tangent line to the parabola y = x 2 at the point (2 , 4). [10 pts] (4) Show that the vector orth a b = b - proj a b is orthogonal to a . [6 pts] (5) Find the angle between a diagonal of a cube and one of its edges. [8 pts]
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Unformatted text preview: (6) Find the cross product a × b and verify that it is orthogonal to both a and b : a = i + 3 j-2 k and b =-i + 5 k . [8 pts] (7) Find parametric and symmetric equations of the line that passes through the point (2 , 1 , 0) and is perpendicular to both i + j and j + k . [6 pts] Additional : Find parametric and symmetric equations of the line of intersection of the planes x + y + z = 1 and x + z = 0. [5 pts] (No partial credit) Show all your work in blue/green book! 1...
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## This document was uploaded on 08/09/2011.

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