Vector

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A vector is a mathematical object that has a size and direction. A vector can be used to show distance and direction. Vectors can be used to show how fast something is moving and in what direction. Vectors can also be used to show many other things.

The simplest picture of a vector is a line segment, with a starting point and an ending point.

[change] Examples of vectors

• For example, if Jane wants to know the position of Sally, Sally can give Jane a vector to show the position. If Jane and Sally are in the world, there are three dimensions. Therefore, Sally gives Jane a list of three numbers to show her position. The three numbers in the vector Sally gives Jane might be:

1. Sally's distance north of Jane
2. Sally's distance east of Jane
3. Sally's height above the earth

• The string of numbers {3, 2, 4) is a three dimensional vector.
• John walks north 20 feet. The direction north together with the distance "20 feet" is a vector.
• An apple falls down at 10 feet per second. The direction down together with the speed "10 feet per second" is a vector.
• The string of numbers (2, 1, 1, 2, 5, 1) is a 6 dimensional vector.

[change] Examples of nonvectors

• A distance with no direction is not a vector. For example, the distance from Jonesville to Smith City is 10 kilometers. The distance between the two places is 10 kilometers. This 10 kilometer distance is not a vector.

• The number of apples in a box is not a vector.

• A person pointing at a building is also not a vector because while there is a direction there is not a magnitude.

• Some simple things, like the length of a rod, can be measured by only giving one number, with the unit of measurement. Such things are called scalars

• Speed is not a vector. Speed is a scalar.

• John is in a car at point A is driving at a certain speed towards B. John tells Sally what speed he is going. John does not tell Sally he is driving towards B. Sally cannot tell where John will be in one hour, since she does not know the direction. Knowing the speed alone is not enough.

Sometimes, only a number for the size is needed. However, the direction is also needed sometimes.

[change] More vectors

• Displacement is a vector. Displacement is the 'distance moved' in a certain direction. Distance alone is a scalar.

• Force is a vector.

• Acceleration is a vector.simple:Vector space