MATH261 EXAM I SPRING 2015
NAME:
CSU ID:
Problem Points
1
2
SECTION NUMBER:
3
4
5
6
You may NOT use calculators or
any references. Show work to receive full credit.
GOOD LUCK !!!
Total
100
Score
1. (a) (8 pts) Find the distance from the point (1, 2, −4) to the plane x + 2y − 2z = 6.
(b) (8 pts) Find the distance from the point (1, 2, −4) to the line given by r(t) =
h1 + 2t, 1 − 2t, −3 + ti.
2. Given the two vectors
A = −2i + 4j − 4k
B = −i + j + k
complete the following:
(a) (8 pts) Find the projection of B onto A.
(b) (8 pts) Find A × B.
(c) (4 pts) Find the area of the triangle with vertices (0, 0, 0), (−2, 4, −4), (−1, 1, 1).
3. Given the lines below, complete the following:
(a) (8 pts) Find the points of intersection.
(b) (8 pts) Find the equation of the plane containing the lines. Your final answer
must be in the form Ax + By + Cz = D.
L1 : r1 (t) = h−2 − t, 2t, 3 + 2ti
L2 : r2 (s) = h4 + s, 6 + 4s, −12 − 3si
4. Given r(t) = (3 cos t)i + 4tj + (3 sin t)k complete the following:
(a) (6 pts) Find v(t), |v(t)|, and a(t)
(b) (4 pts) Write down the integral representing the arc length of the curve from the
point (3, 0, 0) to (−3, 4π, 0) and evaluate it to find the arc length between those
two points.
(c) (4 pts) Find T(t) and T( π2 ).
(d) (2 pts) Find N(t) and N( π2 ).
5. Given a(t) = he2 , 2, −1/(t + 1)2 i, v(0) = h1, 0, −5i, and r(0) = h3, −3, 0i, find the
following:
(a) (8 pts) Find v(t).
(b) (8 pts) find r(t).
6. Evaluate the limit or determine that the limit does not exist. Proper work must be
shown.
x3 + y 3
(x,y)→(0,0) x3 + 3y 3
cos(x2 + y)
(b) (8 pts)
lim π
(x,y)→(0, 2 ) sin(x2 + y)
(a) (8 pts)
lim