Video Transcript
Using the figure, express vector 𝐎𝐂 in component form.
In the figure shown, we have a three-dimensional structure with the points 𝐴, 𝐵, and 𝐶 labeled. It also shows the 𝑥-, 𝑦-, and 𝑧-coordinate axes. We have been asked to express vector 𝐎𝐂 in component form. There will be an 𝑥-, 𝑦-, and 𝑧-component equal to the distance that point 𝐶 is from the origin in those three directions. To travel from the origin to point 𝐶, we travel five meters in the positive 𝑥-direction. We then travel three meters in the negative 𝑦-direction. So the 𝑦-component is negative three. Finally, as point 𝐶 lies in the two-dimensional 𝑥𝑦-plane, the 𝑧-component is equal to zero. The vector 𝐎𝐂, written in component form, is five, negative three, zero.
