using components methods, add the following vectors
`vec(A) = A_(x) hat(i) + A_(y)hat(j) + A_(z) hat(k)`
`vec(B) = B_(x) hat(i) + B_(y) hat(j) + B_(z) hat(k)` .

Explanation

The two vectors `vec(A) and vec(B)` can be expressed as in a Cartesian coordinate system .
`vec(A) = A_(x) hat(i) +A_(y)hat(j) +A_(z) hat(k)`
`vec(B) = B_(x) hat(i) + B_(y) hat(j) + B_(z) hat(k)`
Then the addition of two vectors is equivalent to adding their corresponding x , y and z components .
`:. vec(A) + vec(B) = (A_(x) + B_(y)) hat(i) + (A_(y) +B_(y))hat(j) + (A_(z) + B_(z))hat(k)`