Let and be two arbitrary points in three–dimensional space.

MATHEMATICS · Multi-part · A Level · Mathematics · Vectors · Vectors

Problem

Let

A(x_1, y_1, z_1)

and

B(x_2, y_2, z_2)

be two arbitrary points in three–dimensional space. (i) Define the position vector of a point with respect to the origin

O(0,0,0)

. (ii) Express the vector

\overrightarrow{AB}

in component form in terms of

x_1, y_1, z_1

and

x_2, y_2, z_2

. (iii) Hence show that the magnitude

|\overrightarrow{AB}|

equals

\sqrt{(x_2-x_1)^2+(y_2-y_1)^2+(z_2-z_1)^2}