Video Transcript
Find the unit vector in the direction of the 𝑧- or 𝑧-axis.
We can begin by drawing the three-dimensional coordinate plane where the 𝑥-, 𝑦-, and 𝑧-axes are perpendicular to one another. The unit vector in the direction of the 𝑥-axis is 𝐢. In the direction of the 𝑦-axis, the unit vector is 𝐣. And finally, in the direction of the 𝑧- or 𝑧-axis, the unit vector is 𝐤.
In this question, we’re interested in the 𝑧-axis. Therefore, our vector will be equal to zero 𝐢 plus zero 𝐣 plus one 𝐤. This can be rewritten as one 𝐤 or just 𝐤. Written in component form, the unit vector in the direction of the 𝑧-axis is zero, zero, one. The 𝑥- and 𝑦-components are equal to zero, and the 𝑧- or 𝑧-component equals one.
