Vector addition and subtraction

"In general it is best to conceptualize vectors as arrows in space, and then to make calculations with them using their components. (You must first specify a coordinate system in order to find the components of each arrow.) This problem gives you some practice with the components.

Let vectors (A = 1, 0 -3), (B = -2, 5, 1), and (C = 3, 1, 1). Calculate the following, and express your answers as ordered triplets of values separated by commas."

the first problem is A - B.

could someone please explain the steps so i can do the rest myself? i'm just not getting how the coordinates translate to the examples the professor had in class

to find A-B, just subtract component by component:

A-B = (1-(-2),0-5,-3-1) = (3,-5,-4)

if you were asked to find A+B: (1+(-2),0+5,-3+1)=(-1,5,-2)

Each Vector has a three components in the directions i, j, k [those 3 are known as the unit vectors i.e each one is of magnitude=1]

Now Vector A= 1, 0, -3 i.e: it has components in i and k directions Not in j direction and it is written as follow
A= 1 i - 3 k
and the same for B Vector
B= -2 i + 5 j + 1 k

Adding/subtracting Vectors will be done by adding/subtracting components in the same direction [i or j or k directions]

A-B= [ 1 i - 3 k ] - [ -2 i + 5 j + 1 k ]
A-B=(1-(-2)) i+ (0-5) j + (-3-1) k = 3 i - 5 j - 4 k => (3, -5, -4)