Vectors - Fundamentals and Operations
Student Extras
Need to see it? Study the 6 + 8 = ??? animation from the Multimedia Physics Studios.
Walter Fendt Physics Applets: Resultant of Forces (Addition of Vectors)
Add between two and five vectors together with this interactive Java simulation.
Teacher's Guide
Explore nine lessons from a two-week unit on vectors by the Center for Innovation in Science and Engineering Education (CIESE).
The LaboratoryLooking for a lab that coordinates with this page? Try the As the Crow Flies Lab from The Laboratory.
The LaboratoryLooking for a lab that coordinates with this page? Try the Map Lab from The Laboratory.
Treasures from TPFNeed ideas? Need help? Explore The Physics Front's treasure box of catalogued resources on vectors.
Resultants
The resultant is the vector sum of two or more vectors. It is the result of adding two or more vectors together. If displacement vectors A, B, and C are added together, the result will be vector R. As shown in the diagram, vector R can be determined by the use of an accurately drawn, scaled, vector addition diagram.
To
say that vector R is the resultant displacement of
displacement vectors A, B, and C is to say that a person who
walked with displacements A, then B, and then C would be
displaced by the same amount as a person who walked with
displacement R. Displacement vector R gives the same
result as displacement vectors A + B + C. That is why
it can be said that
A + B + C =
R
The above discussion pertains to the result of adding displacement vectors. When displacement vectors are added, the result is a resultant displacement. But any two vectors can be added as long as they are the same vector quantity. If two or more velocity vectors are added, then the result is a resultant velocity. If two or more force vectors are added, then the result is a resultant force. If two or more momentum vectors are added, then the result is ...
In all such cases, the resultant vector
(whether a displacement vector, force vector, velocity
vector, etc.) is the result of adding the individual
vectors. It is the same thing as adding A + B + C + ... .
"To do A + B + C is the same as to do R." 
As
an example, consider a football player who gets hit
simultaneously by three players on the opposing team
(players A, B, and C). The football player experiences three
different applied forces. Each applied force contributes to
a total or resulting force. If the three forces are added
together using methods of vector addition (discussed
earlier), then the resultant vector R can be determined.
In this case, to experience the three forces A, B and C is
the same as experiencing force R. To be hit by players A, B,
and C would result in the same force as being hit by one
player applying force R. "To do A + B + C is the same as to
do R." Vector R is the same result as vectors A + B +
C!!
In summary, the resultant is the vector sum of all the individual vectors. The resultant is the result of combining the individual vectors together. The resultant can be determined by adding the individual forces together using vector addition methods.