WEBVTT
00:00:01.580 --> 00:00:09.200
Given that vector 𝐀 is equal to two 𝐤, write vector 𝐀 in Cartesian coordinates.
00:00:10.330 --> 00:00:22.140
We begin by recalling that the fundamental unit vectors 𝐢 hat, 𝐣 hat, and 𝐤 hat can be shown on a three-dimensional coordinate plane as follows.
00:00:23.130 --> 00:00:27.360
One unit in the 𝑥-direction is denoted 𝐢 hat.
00:00:28.210 --> 00:00:33.460
In the same way, one unit in the 𝑦-direction is denoted 𝐣 hat.
00:00:34.240 --> 00:00:38.730
And one unit in the 𝑧-direction is denoted 𝐤 hat.
00:00:39.690 --> 00:00:43.860
In this question, vector 𝐀 is equal to two 𝐤.
00:00:44.920 --> 00:00:49.060
This means that its 𝑥- and 𝑦-components are equal to zero.
00:00:50.120 --> 00:01:06.220
When writing a vector in terms of its Cartesian coordinates, the 𝑥-component is the displacement in the 𝑥-direction; the 𝑦-component, the displacement in the 𝑦-direction; and the 𝑧-component, the displacement in the 𝑧-direction.
00:01:07.110 --> 00:01:11.390
As already mentioned, both 𝑥 and 𝑦 are equal to zero.
00:01:12.170 --> 00:01:19.880
As vector 𝐀 is equal to two multiplied by the unit vector 𝐤 hat, 𝑧 is equal to two.
00:01:20.820 --> 00:01:27.820
The vector two 𝐤 written in Cartesian coordinates is zero, zero, two.