MATH 1320 : Spring 2014
Lab 7
Lab Instructor : Kurt VanNess
Name:
Score:
Write all your solutions on a separate sheet of paper.
1. Suppose that a and b are nonzero vectors.
(a) Under what circumstances is compa b = compb a?
(b) Under what circumstances is proja b = projb a?
2. A plane is capable of flying at a speed of 180 km/h in still air. The pilot takes off from an airfield and
heads due north according to the plane’s compass. After 30 minutes of flight time, the pilot notices
that, due to the wind, the plane has actually traveled 80 km at an angle 5◦ east of north.
(a) What is the wind velocity?
(b) In what direction should the pilot have headed to reach the intended destination?
3. A wrench 30 cm long lies along the positive x-axis and grips a bolt at the origin which is sticking into
the y-axis. A force is applied in the direction h−2, 0, 5i at the end of the wrench. Find the magnitude
of the force needed to supply 100 N·m of torque to the bolt.
4. Use the scalar triple product to determine whether the points A(1, 3, 2), B(3, −1, 6), C(5, 2, 0), and
D(3, 6, −4) lie in the same plane. [Hint: You only need to calculate one scalar triple product and you
should not treat the points as vectors.]
5. Let L be the line passing through the origin and the point (2, 0, 0). Find the point of intersection
between L and the plane x − 2y + z = 1.
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