7.3. Resolution of Vectors into Components http://www.ck12.org
7.3 Resolution of Vectors into Components
Here you will find unit vectors and you will convert vectors into linear combinations of standard unit vectors and
component vectors.
Sometimes working with horizontal and vertical components of a vector can be significantly easier than working
with just an angle and a magnitude. This is especially true when combining several forces together.
Consider four siblings fighting over a candy in a four way tug of war. Lanie pulls with 8 lb of force at an angle
of 41◦. Connie pulls with 10 lb of force at an angle of 100◦. Cynthia pulls with 12 lb of force at an angle of
200 ◦. How much force and in what direction does poor little Terry have to pull the candy so it doesn’t move?
Watch This
MEDIA
Click image to the left for use the URL below.
URL: http://www.ck12.org/flx/render/embeddedobject/61370http://www.youtube.com/watch?v=Ect0fBnBlLc James Sousa: The Unit Vector
MEDIA
Click image to the left for use the URL below.
URL: http://www.ck12.org/flx/render/embeddedobject/61372http://www.youtube.com/watch?v=WZ3xzVHT0mc James Sousa: Find the Component Form of a Vector Given
Magnitude and Direction
Guidance
A unit vector is a vector of length one. Sometimes you might wish to scale a vector you already have so that it has
a length of one. If the length was five, you would scale the vector by a factor of^15 so that the resulting vector has
magnitude of 1. Another way of saying this is that a unit vector in the direction of vector→vis|−→−→vv|.