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Introducing vectors for engineering applications
Introducing vectors for engineering applications

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2.4 Position vectors

There is a strong similarity between coordinates and vectors, and we have made use of this similarity when converting between vectors of different forms. We can also make use of this similarity when describing the locations of points in space: the location of a point can be described using a vector.

Let cap p be a point in space. Then the position vector of cap p is a displacement vector times times OP right arrow where cap o is the origin. This is illustrated in Figure 21.

Described image
Figure 21 The position vector times times OP right arrow

The components of the position vector of a point are the same as the coordinates of the point. So the position vector of a point cap p with coordinates left parenthesis x comma y right parenthesis is

equation sequence part 1 times times OP right arrow equals part 2 x times i plus y times j equals part 3 vector element 1 x element 2 y full stop

If a point is denoted by a capital letter, as is the usual convention, then it’s often convenient to denote its position vector by the corresponding lowercase, bold (or underlined) letter. For example, we can denote the position vector of the point cap p by bold p, the position vector of point cap a by bold a, and so on.

Activity 12

Identify the position vectors of the points labelled cap a to cap e in the following diagram.