23 Sample Exam 1B

23 Sample Exam 1B - (d) x 2-4 y 2 = 1 (e) x 2 + y 2-z = 0...

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Practice Midterm I September 25, 2005 1. Let A = 5 j - 3 k and B = i + j + k . Find the following: (a) A · B , | A | , and | B | (b) The cosine of the angle between A and B (c) The scalar projection of B onto A (d) The vector projection of B onto A 2. Given the points P (1 , - 1 , 2), Q (2 , 0 , - 1), and R (0 , 2 , 1), find the following: (a) The area of the triangle determined by P , Q , and R (b) A unit vector perpendicular to the plane PQR 3. Find the parametric and symmetric equations of the line through (1 , 1 , 1) parallel to the z -axis 4. Find the point of intersection of the lines: x = 2 t + 1, y = 3 t + 2, z = 4 t + 3 and x = s + 2, y = 2 s + 4, z = - 4 s - 1 5. Sketch the following surfaces: (a) 16 x 2 + 4 y 2 = 1 (b) y = - ( x 2 + z 2 ) (c) x 2 + y 2 - 16 z 2 = 16
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Unformatted text preview: (d) x 2-4 y 2 = 1 (e) x 2 + y 2-z = 0 6. Translate the point ( r,,z ) = (1 ,/ 2 , 1) into rectangular and spherical coordinates 7. Translate the point ( ,, ) = (2 2 ,/ 2 , 3 / 2) into rectangular and cylindrical coordinates 8. Given r ( t ) = t i + (2 / 3) t 3 / 2 k , 0 t 8, nd the curves unit tangent vector and the length of the indicated portion of the curve 9. Find T ( t ), N ( t ), B ( t ), and for the space curve r ( t ) = ( e t cos t ) i + ( e t sin t ) j + 2 k...
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This note was uploaded on 02/09/2008 for the course MATH 23 taught by Professor Yukich during the Spring '06 term at Lehigh University .

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