Math 150 – Fall 2015: Quiz 11 – Section 9A-9E
Directions: You may work in groups and use your notes to complete this quiz.
1. Find the vector that represents moving from the point P = (−3, 3, 7) to the point Q(−4, 6, 5).
2. Calculate 3h4, −2, 5i − 5h2, −3, −4i + 2h3, 0, 5i. Write your answer in terms of the ~i, ~j, and ~k vectors.
3. Is there a scalar α that solves the equation αh12, −6i = h4, 2i? If yes, then find α.
4. Suppose a bird flies 10 miles in a direction 60◦ north of east. Assuming that the origin is the bird’s
starting point and that east is the positive x-axis, what are the coordinates of the bird’s final location?
5. Find the length of the vector 2h1, 3, −5i − 4h−2, 3, −2i.
6. Find a unit vector which points in the same direction as the vector from the point P (−3, 2) to the
point Q(3, −3).
7. Determine the angle between the vectors h−5, 1i and h2, −3i.
8. Find a unit vector that is perpendicular to the vector h−3, 7i, and the x-coordinate is negative.