Math 206A Quiz 02 page 1 1/28/2011 Name
1. Consider the two lines in R3parameterized by x(t) = โโโโโโโโโโโโโโโโโโ
(50,36,29) + t(10,2,4) and y(s) = โโโโโโโโโโโโโโโโโโโโ
(2sโ10,5sโ22,3sโ17),
respectively.
1a. Itโs a fact that these two lines intersect at some point P. Find P. Show all your work.
1b. What are t0and s0, respectively, so that x(t0) = Pand y(s0) = P?
1c. Since these lines intersect, they belong to the same plane. Find the equation of that plane. Show all your work.
2. Consider an object moving on the path with motion parameterized by f(t) = (tโ2)(tโ3)(tโ4)i+ (0.5t2โ5)j=
(t3โ9t2+ 26tโ24)i+ (0.5t2โ5)jfor tโ[1.5,4.25].
2a. Plot this path on your calculator and make a careful copy of
that plot on the axes provided here. Note the start and endpoints
are already on the plot.
2b. Find all the times tat which the object crosses the yaxis.
2c. When it makes the second crossing, what is the ycoordinate at that time?
2d. What is the velocity vector when the object crosses the yaxis the first time? Show all your work.
2e. BONUS: To two decimal places, find all times tat which the object is moving in the direction โโโโ
(1,1).