MATH 240 Midterm: MATH240 math240spring2012M2-Solution

• School: Simon Fraser University
• Department: Mathematics
• Course: MATH 240
• Professor: All

Document Summary

Solution set, math 232 midterm 2, version 1 (green/grey) = 15 i + j + 10 k (cid:12)(cid:12)(cid:12)(cid:12)(cid:12)(cid:12) (u u) v = 0 v. = 0 where the rst step uses the fact that cross product of two parallel vectors is the zero vector. You can also get the right answer by calculating directly. =(cid:12)(cid:12)(cid:12)(cid:12)(cid:12)(cid:12) (cid:12)(cid:12)(cid:12)(cid:12)(cid:12)(cid:12) (we have used the fact that a b = b a. We then use the value of u v from part (a). You can also get the correct answer by calculating directly. ) The area of the parallelogram is ||u v||. We use the value of u v from part (a) to see that this is ||(15, 1, 10)|| = 152 + 12 + 102 = 326. Note that | 3 + i| =q( 3)2 + 12 = 3 + 1 = 2, so we can write where cos = 3/2 and sin = 1/2, so = /6.