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# Vectors

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by

## Joel Kliewer

on 30 April 2014

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#### Transcript of Vectors

Vectors
A Vector is a quantity with both direction and magnitude.
What is a Vector?
Magnitude and Direction
Examples
35 degrees
North of East
4.5 in
Magnitude describes a vector with a measurement. Some common measurements would be length, speed, or time.

Direction of a vector is where the vector is headed by using north, south, east, or west with a degree of angle. Because we use these 4 directions we never have a degree over 90 degrees.
vector 1
Vector 2
Resultant Vector 1
Resultant Vectors
A resultant vector is exactly what it sounds like. When two vectors are added or combined together, the line that makes the connection of the two is the resultant vector.
How Vectors are Applied
When engineers are designing tall structures, they need to take many variables into account so that they know the building will be structurally sound. Some variables would be wind and gravity.
Sail Boats
When sailing there is a wide range of vectors as well. Rather it be the current of the ocean, wind, angle of sail or the rudder, all things have a large impact on sailing.
Airplanes
Here the plane is traveling 150 mph N and the wind is going 45 degrees S of E at 25 mph. The resultant vector is the path of the plane.
Subtracting Vectors

The easy way to remember about subtracting vectors is to know that they're just flipped. In the picture above it shows how vector
b
would be if we subtracted or added.
Magnitude
Direction
In the Picture above, the arrows represent how the air
flows over the wing and how that can help the airplane
lift in to the air.
The Vectors would be the wind, and the original path
of the plane or wing. The Resultant vector is the path
of the plane after the lift.
In the picture below you can see the flap on the back of the wing. The flaps control how planes turn, dive or ascend into the unknown.

If the flap were to tilt upward, the wind (vector) moving over the wing would hit the flap and make the plane descend (resultant vector) from its previous path (vector).
To find the magnitude and direction of the resultant vector, we would use the law of cosines. After working it we get that the magnitude would be 133.5 MPH.
Vectors
By: Joel Kliewer
Full transcript