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SECTION 3.3
SCALAR MULTIPLICATION:
3
2
1
−
6
2
=
−
Let
u be a vector; let c be a
scalar; and set
v = cu.
(1) If c > 0, then v is in the
same direction as u.
(2) If c < 0, then v is in the
opposite direction from u.
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View Full Document The length or magnitude of a
vector
1
2
u
u
u
=
is
22
12
uu
u
=+
Example:
If
uA
B
=
!!!"
where
A=(3, 4) & B = (5, 1),
find
u
53
2
14
5
u
−
==
−−
−
() ( )
25
u
−
42
5
2
9
=
(3)
vc
u
=
u
2u
(1/2)u
The vectors
u
and
v
are
parallel
provided there is a
nonzero scalar c such that
v = cu.
Given that u & v are parallel,
find a if
4
a
v
=
and
3
2
u
=
−
So we know that v = cu
3
42
a
c
=
−
3
ac
c
=
−
4 = 2c means c = 2
So a = 6
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View Full Document DEFN: A vector
u
is a unit
vector
provided
1
u
=
Example:
1
2
3
2
u
=
is a unit
vector because
2
2
13
22
u
=+
11
44
=
=
Let
v
be a nonzero vector.
Then
1
uv
v
=
is a unit vector in the same
direction as u.
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This note was uploaded on 11/11/2008 for the course MATH 1114 taught by Professor Jhengland during the Fall '08 term at Virginia Tech.
 Fall '08
 JHENGLAND
 Linear Algebra, Algebra, Multiplication, Scalar

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