This is a very simple post and a very simple subject, but every once in a while even the experts need to be reminded how to do simple addition and subtraction with vectors.  Let’s go ahead and specify a couple vectors that we can work with.

Vector $A = u_{x} + 2 u_{y} + 3 u_{z}$

In MATLAB: >>A = [1 2 4];

Vector $B = 2 u_{x} + 3 u_{y} + 4 u_{z}$

In MATLAB: >>B = [2 3 4];

When you add vectors together, you add each individual directional component ( $u_{x}, u_{y}, u_{z}$).  Subtraction works the exact same way.  Lets go ahead and do a few, C will represent the vector that results from the addition and subtraction. $C = A + B = (2 + 1) u_{x} + (2 + 3) u_{y} + (3 + 4) u_{z} = 3 u_{x} + 5 u_{y} + 7 u_{z}$ $C = A - B = (2 - 1) u_{x} + (2 - 3) u_{y} + (3 - 4) u_{z} = u_{x} - u_{y} - u_{z}$

These vectors are all in 3-dimensional space with a X, Y and Z component.  The number in front of each $u_{..}$ directional component is the weight or magnitude of that particular directional component of the vector.  There it is, short and sweet 🙂