23 Sample Exam 1B - Practice Midterm I 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

# 23 Sample Exam 1B - Practice Midterm I 1 Let A = 5 j 3 k...

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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