6.2 Vector Addition
Geometric Vectors
Algebraic Vectors
VECTOR Resources
vector resources link
teacher tube ­ vector addition
Because non­zero vectors have direction as well as magnitude, adding vectors involves more than simply adding numbers. The sum of two vectors is another vector.
There are two equivalent procedures for addition of vectors
a) the Triangle Law b) the Parallelogram Law
Triangle Law of Vector Addition
Let a and b be any two vectors.
b
a + b
a
Arrange them head­to­tail.
The sum, a + b, is the vector from the
tail of one vector to the head of another.
b
a + b
a
a
a + b
b
b
a + b
a
Resultant Vector the vector that results from adding two or more vectors
a + b
This is the resultant vector.
Parallelogram Law of Vector Addition
Let a + b be any two vectors.
Arrange them tail­to­tail.
a + b
Construct a parallelogram and the diagonal from where the The sum, a + b, is the vector with the
same tail as a and b with its head at
the opposite vertex of the parallelogram.
b
a
Can you show the following property? If not, explain why.
b
a + b
| a + b | = | a | + | b |
a
| a + b | > | a | + | b |
| a + b | < | a | + | b |
Properties of Vector Addition ­ Commutative Law
?
a + b = b + a
Properties of Vector Addition ­ Associative Law
?
(a + b) + c = a + (b + c ) Properties of the Zero Vector
a + 0 = a
Every vector, a, has an opposite vector ____ such that
a + ____ = 0
Subtraction of Vectors Link
Example 1
THE ANGLE BETWEEN TWO VECTORS
The angle between two vectors is the angle when they are placed tail to tail.
Trigonometry can be used to determine this angle.
Example 3
Determine the magnitude and direction of the sum of two vectors u and v, if their magnitudes are 5 and 8 units, respectively, and the angle between them is 30o.
Homework
p. 290 #1 ­ 8, 10, 12 ­ 14
Write down the Key Concepts and Need to Know from the end of 6.2.