Component form of a vector with initial point and terminal point
Basic relation. To find the coordinates of the vector AB , knowing the coordinates of its initial point A and terminal point B is necessary subtract the appropriate coordinates of initial point from terminal point.
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Formulas determining coordinates of a vector by given coordinates of its initial and terminal points
Vector coordinates formula for plane problems
In the case of the plane problem the vector AB set by the coordinates of the points A(Ax ; Ay) and B(Bx ; By) can be found using the following formula
AB
= {B
x
– A
x
; B
y
– A
y
}
Vector coordinates formula for spatial problems
In the case of the spatial problem the vector AB set by the coordinates of the points A(Ax ; Ay ; Az) and B(Bx ; By ; Bz) can be found using the following formula
AB
= {B
x
– A
x
; B
y
– A
y
; B
z
– A
z
}
Vector coordinates formula for
n
dimensional space problems
In the case of the n dimensional space problem the vector AB set by the coordinates of the points A(A1 ; A2 ; … ; An) and B(B1 ; B2 ; … ; Bn) can be found using the following formula
AB
= {B1 – A1 ; B2 – A2 ; … ; B
n
– A
n
}
