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**Vectors** have *magnitude* and *direction*. The magnitude of
is written
|| *v* . Position, displacement, velocity,
acceleration and force are examples of vector quantities. Vectors have the
following properties:

- 1.
- Vectors are equal if they have the same
*magnitude*and*direction*. - 2.
- Vectors must have the same units in order for them to be added or subtracted.
- 3.
- The negative of a vector has the same magnitude but opposite direction.
- 4.
- Subtraction of a vector is defined by adding a negative
vector:
- = + (- )

- 5.
- Multiplication or division of a vector by a scalar
results in a vector for which
- (a)
- only the magnitude changes if the scalar is positive
- (b)
- the magnitude changes and the direction is reversed if the scalar is negative.

- 6.
- The projections of a vector along the axes of a rectangular
co-ordinate system are called the
**components**of the vector. The components of a vector completely define the vector.

cos = *A*_{x}=*A*cossin = *A*_{y}=*A*sin*A*and as functions of*A*_{x}and*A*_{y}. By Pythagoras we have,

*A*=

tan = = . - 7.
- To add vectors by components:
= + + +...
- (a)
- Find the components of all vectors to be added.
- (b)
- Add all
*x*components to get*R*_{x}=*A*_{x}+*B*_{x}+*C*_{x}+ ...

Add all*y*components to get*R*_{y}=*A*_{y}+*B*_{y}+*C*_{y}+... - (c)
- Then

|| = = .

10/9/1997