Vectors

A vector is formally defined as an element of a vector space.

A zero vector, denoted , is a vector of length 0, and thus has all components equal to zero.

Two Fundamental Definitions:

•  Two vectors, A and B are equal if they have the same magnitude and direction, regardless of whether they have the same initial points.

              

•        A vector having the same magnitude as A but in the opposite direction to A is denoted by -A

Graphical Vector Addition

Adding two vectors A and B graphically can be visualized like two successive walks, with the vector sum being the vector distance from the beginning to the end point. Representing the vectors by arrows drawn to scale, the beginning of vector B is placed at the end of vector A. The vector sum R can be drawn as the vector from the beginning to the end point.

SAMPLE PROBLEMS

1. You travel for 3.0 m/s in an angle of 45 deg (North of East) and then proceeded to 5.0 m/s, 135 deg (North of West). How far from where you started did you end up? Draw the vector and indicate the scale you used.

Therefore, your resultant vector would be 5.83 m/s, 104 deg (North of West).

2. You are jogging at the speed of 4.0 m/s, 135 deg (North of West)  and then turned south of east at 4.0 m/s, 315 deg. How fast from where you started did you end up? Draw the vector and indicate the scale used.

Therefore, your resultant vector would be 0 m/s since they have different directions and the same magnitude. 

3. I am riding a bike at 7.0 m/s at the east and then going to the north at 2.0 m/s. How fast from where I started did I end up? Draw the vector and indicate the scale used. 

I traveled for 7.28 m/s at an angle of 15.9 deg, North of East.

4. My sister walked at 4.0 m/s, North and turned East at  2.0 m/s. She then walked farther at 2.0 m/s at an angle of 210 deg (South of West). How fast from where she started did she end up?

She walked at 3.01 m/s at an angle of 84.9 deg, North of East.

APPLICATIONS OF VECTORS IN EVERYDAY LIFE

You can consider throwing a Frisbee disc or javelin, a hockey bank shot off the boards, football (soccer) ball dynamics, airplane course and speed through the air with wind, playing pool or billiards, the course and speed a baseball fielder must go to intercept the fly ball, and even the course and speed an interceptor must fly to meet an airliner that has been hijacked.

In everyday life, in going to school, crossing the streets, that alone is related to vectors. Also when my mom drives me from school on the way home, that could also be an application of vectors in daily routine.  

So far, so great! These are what I've learned so far about vectors. Thanks for viewing this post! :)

Sources:

http://www.physicsclassroom.com/morehelp/vectaddn/practice.cfm#4

http://mathworld.wolfram.com/Vector.html

http://hyperphysics.phy-astr.gsu.edu/hbase/vect.html

http://www.physics.uoguelph.ca/tutorials/vectors/vectors.html