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Vectorsscalar quantities
• magnitude
• mass• temperature• electric potential
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vectors• magnitude &
direction• bold face in text
• force• heat flux• electric field• magnetic field
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AAuA
AAu
2z
2y
2x AAA A
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zyx uuuA 1243
131243 222 A
131243 zyx
Auuu
u
AAuA
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MATLAB
• A = [Ax Ay Az];• norm (A)
• A = [3 4 12];• a = norm (A);• a• 13
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A+B
A
B
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A-B
A
B
-B
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zyx uuuA 543
zyx uuuB 321
zyx uuuBA 864
zyx uuuBA 222
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• a = 1ux + 2uy + 3uz
• b = 3ux + 2uy + 1uz
• c = a + b • c = 4ux + 4uy + 4uz
• >> a = [1 2 3];• >> b = [3 2 1];• >> c = a + b;• c =• 4 4 4
vectors - addition
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cosABBA
B
A
ABBA
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cosABBA
0if BAB
A
2
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zyx uuuA 543
zyx uuuB 321
261583 BA
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cosABBA
B
A
AB
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zzz cosAA uA
x y
z
xx y
y
z
z A
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MATLAB
• dot (A, B)
• A = [1 2 3];• B = [2 3 4];• c = dot (A, B);• c• 20
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BAuBA sinAB
x y
z
AB
BAu
BAu
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ABuAB sinBA
x y
z
A B
ABu
BAu
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BAuBA sinAB
x y
z
0BAif
AB
πθ0θ
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BAuBA sinAB
x y
z A
B
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x y
z A
B
BAuBA sinAB
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x y
z A
B
BAuBA sinAB
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x y
z A
B
area = AB sin
BAuBA sinAB
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xuA yuB
xu00 yu00 zu01
010001
zyx uuuBA
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MATLAB• A = [1 0 0];• B = [0 1 0];
• c = cross (A, B);• c• 0 0 1• d = cross (B, A);• d• 0 0 -1
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intersection of 3 planes
x
y
z
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zyx uuuA zyx AAA
zyx uuuB zyx BBB
zzyyxx BABABA BA
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zyx uuuA zyx AAA
zyx uuuB zyx BBB
zyx
zyx
zyx
BBBAAAuuu
BA
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intersection of 2 planes
and a cylinder
x
y
z
z
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r
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There are MATLAB commands that permit you
to go back and forth between different
coordinate systems.
They are listed in the text for this class.
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h2 d
h1 d
h3 d
11dh
2211 dhdh
332211 dhdhdh