Quiz_1_20C

Quiz_1_20C - t . 6. Draw the curve C : x = x ( t ) ,y = y (...

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Math 20C (Shenk). Quiz 1. August 9, 2010. Name Section number Work alone and use no books, notes, or calculators. Put your work on 8.”‘ × 11” paper and staple it to the quiz when you turn it in. 1. Find the magnitude and an angle of inclination of the resultant (sum) F of the force vectors F 1 = a 7 , 1 A (pounds) and F 2 = a− 11 , 5 A (pounds). 2. What is the angle θ at P (0 θ π ) in the triangle with vertices P = (1 , 1 , 2) ,Q = (2 , 4 , 3) and R = (0 , 1 , 5)? 3. Give parametric equations of the line L through P = (1 , 2 , 3) and Q = (5 , 2 , 1). 4. (a) Calculate a 1 , 2 , 3 A×a 2 , 1 , 0 A . (a) Two sides of a triangle are formed by the vectors a 1 , 2 , 3 A and a 2 , 1 , 0 A . What is its area? 5. Give an equation of the plane through the point (3 , 2 , 1) and perpendicular to the line x = 5 + 4 t,y = 6 + 3 t,z = 7 + 2
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Unformatted text preview: t . 6. Draw the curve C : x = x ( t ) ,y = y ( t ) , t 3, where x = x ( t ) and y = y ( t ) are the functions of Figures 1 and 2. t 1 2 3 x 5 5 x = x ( t ) t 1 2 3 y 5 5 y = y ( t ) FIGURE 1 FIGURE 2 7. The curve C : x = 3 t t 2 ,y = t 3 3 t 2 + 1 , . 8 t 3 . 25 is shown in Figure 3. (a) Find its velocity vector at t = 1 and draw it with the curve. Use the scales on the axes to measure the components of the vector. (b) Give a denite integral that equals the length of the curve. Do not simplify the integrand or evaluate the integral. x 4 4 y 4 4 FIGURE 3 1...
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