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Name
Math5BF08
Midterm I
A
Work in the space provided (you may use the back). No books, notes, or calculators.
5 problems on 5 pages, 95 points, 5 bonus points for clean and neat work.
Always show work and/or reasoning.
Circle your ﬁnal answer!
Problem 1 (25 pts: 11,6,8)
(a)
The points (0
,
0
,
0)
,
(1
,
0
,

1), and (2
,
1
,
2), form the vertices of a space triangle. Find its area.
(b)
The vector
~
F = 2
b
i
i
b

3
b
j
j +
b
k
b
k
b
k represents a force; what is its scalar component (=scalar projection)
in the direction of 3
b
i
b
i
i + 4
b
k
b
k
b
k?
(c)
An origin vector in the ﬁrst octant makes the same angle with each of the three coordinate axes.
What is the angle? [Write it in the form cos

1
(
α
).]
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View Full Document Problem 2 (21 pts: 10,7,4)
Consider the plane
P
: 2
x

3
y

z
= 14.
(a)
Find the point P
0
where a line passing through P
1
: (1
,
0
,
2) and perpendicular to
P
intersects
P
.
(b)
Find the equation of a plane
P
0
parallel to
P
and passing through P
1
. [Write the equation in the
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This note was uploaded on 03/01/2009 for the course MATH 5B taught by Professor Rickrugangye during the Spring '07 term at UCSB.
 Spring '07
 RickRugangYe
 Math, Vector Calculus

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