Question Video: Using a Graph to Express a Vector in Its Component Form Mathematics • Third Year of Secondary School

Video Transcript

Using the graph, find the vector 𝐎𝐀 in component form.

We begin by recalling that if point 𝐴 has coordinates 𝑥, 𝑦, 𝑧, then vector 𝐎𝐀 has components 𝑥, 𝑦, 𝑧. This is known as the position vector of point 𝐴, where 𝑥, 𝑦, and 𝑧 are the displacements from the origin in these three directions. In this question, point 𝐴 lies on the 𝑦-axis. This means that the 𝑥- and 𝑧-coordinates of point 𝐴 will be equal to zero. And as the point lies at five on the 𝑦-axis, its 𝑦-coordinate will be equal to five. Point 𝐴 has coordinates zero, five, zero. And we can therefore conclude that vector 𝐎𝐀 is equal to zero, five, zero.