16.360 Lecture 13

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16.360 Lecture 13

• Today

Basic Laws of Vector Algebra
Scalars
e.g. 2 gallons, 1,000, 35ºC
Vectors
e.g. velocity 35mph heading south 3N
force toward center
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16.360 Lecture 13

• Cartesian coordinate system

z
A
?
y
?
x
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16.360 Lecture 13

• Vector addition and subtraction

C BA A B,
A
C
C
parallelogram rule
A
head-to-tail rule
C BA A B,
B
B
D A - B -(B A),
A
A
D
D (B-A)
B
B
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16.360 Lecture 13

• position and distance

z
A
B
y
D A - B -(B A),
x
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16.360 Lecture 13

• Vector multiplication

1. simple product
2. scalar product (dot product)
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16.360 Lecture 13
Properties of scalar product (dot product)
a) commutative property
b) Distributitve property
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16.360 Lecture 13
3. vector product (cross product)
a) anticommutative property
b) Distributitve property
c)
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16.360 Lecture 13
3. vector product (cross product)
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16.360 Lecture 13
Example vectors and angles

• In Cartesian coordinate, vector A is directed
  from origin to point P1(2,3,3), and vector B is
  directed from P1 to pint P2(1,-2,2). Find
• (a) Vector A, its magnitude A, and unit vector
  a
• (b) the angle that A makes with the y-axis
• (c) Vector B
• (d) the angle between A and B
• (e) perpendicular distance from origin to vector
  B

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16.360 Lecture 13
4. Scalar and vector triple product
a) scalar triple product
b) vector triple product
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16.360 Lecture 13
Example vector triple product
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