Adding vectors results in a new Resultant Vector. Geometric and Algebraic vectors can be added using different techniques.
Algebraic vectors can be added by adding the respective components along each axis:
\( \vec{a} = \left<3,4\right>, \; \vec{b} = \left<-4,10\right> \)
\( \vec{a} + \vec{b} = \left<3 + -4, 4 + 10\right> = \left<-1, 14\right> \)
Recall the vector addition rules:
| Commutative Law of Addition | \(\vec{u} + \vec{v} = \vec{v} + \vec{u}\) |
| Associative Law of Addition | \( (\vec{m} + \vec{n}) + \vec{o} = \vec{m} + (\vec{n} + \vec{o})\) |
Like adding Algebraic vectors, subtract the respective components along each axis:
\( \vec{a} = \left<3,4\right>, \; \vec{b} = \left<-4,10\right> \)
\( \vec{a} - \vec{b} = \left<3 - (-4), 4 - 10\right> = \left<7, -6\right> \)
You can think of subtracting vectors as adding the Opposite vector:
\( \vec{a} - \vec{b} = \vec{a} + (-\vec{b}) \)
\( = \left<3,4\right> + (-\left<-4,10\right>) \)
\( = \left<3,4\right> + \left<4,-10\right> \)
\( = \left<3+4,4-10\right>\)
\( = \left<7,-6\right>\)
Enter in two vectors below. Then, Click the + button to toggle between addition and subtraction.