8/14/2015
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T: +27(0)51 401 9111

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MATM1544
LECTURE 16
Scalar multiplication
and vector
components
August 14, 2015
T: 051 401 9111
[email protected]
CONTENT
•
Multiplying by a scalar
•
Vector components
•
Examples
•
Exercises
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When adding two vectors along the same line, the
triangle collapses into a single line:
The vector
°
+ ±
now has magnitude
° + ±
,
i.e. we simply
add the two magnitudes together if the two point in the
same direction.
MULTIPLYING BY A SCALAR
Adding
°
to itself:
The vector
2°
has magnitude
2°,
and is in the same
direction as
°
.
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In general we have the rule
•
When a vector
²
is multiplied by a scalar
³,
the vector
³°
has as magnitude
the magnitude of
°
times
³
,
i.e.
³ °.
•
If
³ > 0,
then
³°
is in the same direction as
°
.
•
If
³ < 0,
then
³°
is in the opposite direction than
°
.
e.g.
−0,5°
is in the opposite direction than
°
Magnitude is
0,5=0,5
times that of
°
.
VECTOR COMPONENTS
Components of
°
:
Two vectors which add up to
°
.
°
´
and
°
µ
are components
of
°
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Components are not unique:
Use rectangular components:
Choose
¶

axis and
·

axis
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 Addition, Multiplication, Vector Space