   # Vectors   Note: Vectors are indicated using the "bold-letter" notation.

Q:    How do you geometrically subtract two vectors?

A:    If you have two vectors a and b and want to subtract them.  First you need to reverse the direction of vector b so that it becomes vector -b.  Then you would take vector -b and  place its tail at the end of vector a.  Then you would draw a line from the tail of a to the head of -b.   This line is your new vector with its head at the head of -b.

Example: If we have vector a and want to subtract vector b.  First we reverse the direction of b.   This will give us -b which we can then add to a. => Now we place the tail of vector -b at the head of vector a.   A new vector, d, can be drawn from the tail of vector a to the head of vector -b.

#### + = Q:    How do you geometrically add two vectors?

A:    If you have two vectors a and b and want to add them.  Then you would take vector b and place its tail at the end of vector a.  Then you would draw a line from the tail of a to the head of b.   This line is your new vector with its head at the head of b.

Example: If we have a vector a and want to add it to a vector b.  We place the tail of vector b at the head of vector a.  A new vector, c, can be drawn from the tail of vector a to the head of vector b.

## References

### Components of a Vector A two dimensional vector a has two components, ax and ay, the values for these components are found by drawing lines from the end of a to the coordinate axis.  Thus     ax  = a cos and   ay = a sin where is the angle from the positive direction of the x-axis to the direction of a.  Given the components of a vector we can reconstruct the vector from ### Unit Vectors Unit vectors are vectors with a magnitude of one and pointing in a particular direction.  The sole purpose of unit vectors is specify direction.  In the Three Dimensional Cartesian System: is the unit vector in the positive x direction is the unit vector in the positive x direction is the unit vector in the positive x direction        A vector can be decomposed into its , , and components by breaking the vector into magnitudes on the x, y, and z axis respectfully.

# Mechanics List of Topics

 Measurements Newton's Laws Potential Energy and Conservation of Energy Rotation of Rigid Bodies Elasticity Vectors Forces and Fields Linear Momentum Angular Momentum Mechanical Oscillations Motion of Point-Mass Objects in One Dimension The Gravitational Field Collisions Torque Mechanical Waves Motion of Point-Mass Objects in Two and Three Dimensions Kinetic Energy and Work Circular Motion of Point-Mass Objects Equilibrium Sound  ครั้งที่

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