MAT-2130 Midterm: MATH 2130 App State Spring2011 Test2 answer key
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Be sure to show your work! projv(u) = u v. |r (t)| (cid:19) t(t) +(cid:18) |r (t) r (t)| r (t) = (cid:18) r (t) r (t) Is this angle right, acute, or obtuse ? (circle your answer. ) (d) find the volume of the parallelepiped spanned by u, v, and w. (e) a and b are vectors. Match the following: a b = 0 a b = 0 a (b b) = 0 a and b are orthogonal. This is always true. a and b are parallel. Determine if 1 and 2 are the same, parallel, intersecting, or skew. /10 points) consider the curve r(t) = h5 sin(t), 4 cos(t), 3 cos(t)i where 0 t 2 . Note: the original problem had , 2 cos(t), instead of , 4 cos(t), which leads to an integral which can"t be done by hand. (a) find a formula for this curve"s arc length function: s(t).
