MA 227-6D Spring 2006 Test 1: Vector Calculus, Exams of Advanced Calculus

The spring 2006 ma 227-6d test 1 in vector calculus. The test consists of two parts. Part 1 has five problems worth 4 points each, with no partial credit. Part 2 has two problems worth 10 points each, where partial credit is awarded. The solutions must include enough detail to justify any conclusions.

Typology: Exams

2012/2013

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SPRING 2006 โ€” MA 227-6D โ€” TEST 1
Name:
1. Part I
There are 5 problems in Part 1, each worth 4 points. Place your answer on the line to the
right of the question. No partial credit will be given on Part 1 problems, only your answer
on the answer line will be graded.
(1) Find the dot product of the vectors h2,5,2iand h1,โˆ’2,โˆ’1i.
(2) Find the cross product of the vectors h0,4,โˆ’3iand hโˆ’1,0,1i.
(3) Find the derivative of the vector function h1, t, t2i.
(4) Find the derivative of the vector function hcos t, cos(2t), t sin ti.
(5) Compute R3
0h2,1 + t, etidt.
1
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Name:

  1. Part I

There are 5 problems in Part 1, each worth 4 points. Place your answer on the line to the right of the question. No partial credit will be given on Part 1 problems, only your answer on the answer line will be graded.

(1) Find the dot product of the vectors ใ€ˆ 2 , 5 , 2 ใ€‰ and ใ€ˆ 1 , โˆ’ 2 , โˆ’ 1 ใ€‰.

(2) Find the cross product of the vectors ใ€ˆ 0 , 4 , โˆ’ 3 ใ€‰ and ใ€ˆโˆ’ 1 , 0 , 1 ใ€‰.

(3) Find the derivative of the vector function ใ€ˆ 1 , t, t^2 ใ€‰.

(4) Find the derivative of the vector function ใ€ˆcos t, cos(2t), t sin tใ€‰.

(5) Compute

0 ใ€ˆ^2 ,^ 1 +^ t,^ e

tใ€‰dt.

1

  1. Part II

There are 2 problems in Part 2, each worth 10 points. On Part 2 problems partial credit is awarded where appropriate. Your solution must include enough detail to justify any conclusions you reach in answering the question.

(1) A parallelepiped is spanned by the vectors ใ€ˆ 4 , 2 , 2 ใ€‰, ใ€ˆ 0 , โˆ’ 1 , 1 ใ€‰, and ใ€ˆ 2 , 1 , โˆ’ 1 ใ€‰. Find volume and surface area of the parallelepiped.