# Question Video: Expressing a Point in terms of its Vector Components Mathematics • 12th Grade

Using the graph, express point π΄ in terms of its components.

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### Video Transcript

Using the graph, express point π΄ in terms of its components.

We know that any point in the three-dimensional coordinate plane can be written in the form π₯, π¦, π§. And for any point with coordinates π₯, π¦, π§, the vector ππ has components π₯, π¦, π§, where these components are the displacements of point π΄ in the π₯-, π¦-, and π§-directions from the origin. This is also known as the position vector of point π΄.

In this question, point π΄ lies on the π§-axis. This means that both its π₯- and π¦-coordinates will be equal to zero. From the graph, we can see that we need to move one unit in the positive π§-direction to travel from the origin to point π΄.

We can therefore conclude that point π΄ has coordinates zero, zero, one and the position vector of point π΄ is therefore also equal to zero, zero, one.