CME 100
Fall 2010
Vector Calculus for Engineers
Page 1 of 2
Prof. Eric Darve
Homework 2 – Due 10/6
Read the instructions for doing homeworks in the course information handout. You can find this document
on
coursework
. Don’t forget to write down on your paper the names of the members of your team and their
role. For all questions, show your work and explain your reasoning.
MATLAB Workbook:
Exercises 16
Exercises:
1. Give a geometric description of the set of points whose coordinates satisfy the equations:
x
2
+
y
2
+
z
2
=
4
,
y
=
x
2. Find a vector of length 5 in the direction of (8
,
1
,

5).
3. The wind exerts a 1000 N force on the sail of a boat. How much work did the wind perform in moving
the boat forward by 1 km? Give your answer in N m.
Center line of the boat
Sail
~
F
θ
=
60
◦
4. Consider a circle with center
O
.
AB
is a diameter. The point
C
is on the circle. Using dot products
show that
CA
is orthogonal to
CB
. Hint: use the origin and vector
→
CO
.
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 '08
 DARVE,KHAYMS
 Dot Product, Prof. Eric Darve

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