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Math 23  Quiz 1
September 13, 2007
Solutions
1. Determine whether the vectors
a
=
<
6
,
4
,

2
>
and
b
=
<

2
,

6
,
3
>
are orthogonal,
parallel, or neither.
Solution:
a
•
b
=

12

24

6
6
= 0, so a and b are not orthogonal.
a
×
b
6
= 0, so a and b are not parallel.
Therefore, neither.
2. Find the scalar and vector projections of
b
=
<
1
,
6
,

2
>
onto
a
=
<
2
,

3
,
1
>
.
Solution:
comp
a
b
=
a
•
b

a

=
2

18

2
√
4 + 9 + 1
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Unformatted text preview: =18 √ 14 proj a b = a • b  a  2 a =18 14 < 2 ,3 , 1 > = <18 / 7 , 27 / 9 ,9 / 7 > 3. Find a vector orthogonal to the plane through the points P (2 , ,3), Q (3 , 1 , 0), R (5 , 2 , 2). Solution: PQ = < 1 , 1 , 3 > and PR = < 3 , 2 , 5 > PQ × PR = <1 , 4 ,1 >...
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This note was uploaded on 02/09/2008 for the course MATH 23 taught by Professor Yukich during the Spring '06 term at Lehigh University .
 Spring '06
 YUKICH
 Vectors

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