Question

A vector has co-ordinates (1,1,2) for initial point and (2,1,3) as the terminal point. The length of the vector is

Answer 1

Explanation:

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 = {Bx - Ax ; By - Ay}

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 = {Bx - Ax ; By - Ay ; Bz - Az}

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 ; ... ; Bn - An}

Answer 2

Question

A vector has co-ordinates (1,1,2) for initial point and (2,1,3) as the terminal point. The length of the vector is

Solution

A)

A = i + j + 2k

B)

B = 2i +j +3k

Distance between a and b is the length of a vector

=( 2-1)i +(1-1)j +(3-2)k

= i +k

Magnitude : √ 1 + 1 = √2