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

Using the graph, express point 𝐴 in terms of its components.

01:22

Video Transcript

Using the graph, express point 𝐴 in terms of its components.

We know that any point in the three-dimensional coordinate plane can be written in the form 𝑥, 𝑦, 𝑧. And for any point with coordinates 𝑥, 𝑦, 𝑧, the vector 𝐎𝐀 has components 𝑥, 𝑦, 𝑧, where these components are the displacements of point 𝐴 in the 𝑥-, 𝑦-, and 𝑧-directions from the origin. This is also known as the position vector of point 𝐴.

In this question, point 𝐴 lies on the 𝑧-axis. This means that both its 𝑥- and 𝑦-coordinates will be equal to zero. From the graph, we can see that we need to move one unit in the positive 𝑧-direction to travel from the origin to point 𝐴.

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

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