Quiz #1
September 5, 2007
Name:
MATH 151
This quiz is due by 5pm on Wednesday, September 5. You can turn it in to my office ( Blocker
640d), place it in my mailbox (Blocker 603), e-mail a pdf version to me, or fax it to 979-862-4190.
To receive full credit, all necessary work must be shown.
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1. Given the points P (1, −4) and Q(5, 3) find a unit vector that is in the same direction as QP .
2. Two tug boats are towing a large ship into port. The larger tug exerts a force of 4000 pounds
on its cable, and the smaller tug exerts a force of 3200 pounds on its cable. If the ship is
to travel in a straight line, find the angle θ that the larger tug must make if the smaller tug
makes an angle of 30o .
30
o
3. A wagon is pulled a distance of 100m along a horizontal path by a constant force of 50N. The
handle of the wagon is at an angle of 25o above the horizontal. How much work is done?
4. Find the value of x so that vector projection of b =< x, 7 > onto a =< 1, 4 > is < 5, 20 >
5. Find a vector equation for the line passing through the points A(1, 10) and B(3, 16).
6. Does the point (41, 103) lie on the line represented by the vector equation
r(t) =< 1 + 2t, 3 + 5t >? justify your answer.
7. Here are two lines represented by the vector equations, L1 and L2 .
L1 (t) =< 1 + t, 8 + 3t >
L2 (s) =< 3 − s, 7 − 2s >
(a) Determine if these lines are parallel, perpendicular, or neither.
(b) If the lines are not parallel, then find the angle θ, where 0 < θ ≤ π2 , that is made at the
intersection of the two lines.