WEBVTT
00:00:00.520 --> 00:00:09.240
Given that vector 𝐀 is equal to nine 𝐢 plus three 𝐣 plus seven 𝐤, write vector 𝐀 in Cartesian coordinates.
00:00:10.320 --> 00:00:15.800
Vector 𝐀 is currently written in terms of the fundamental unit vectors 𝐢 hat, 𝐣 hat, and 𝐤 hat.
00:00:16.240 --> 00:00:21.480
These can be shown on the three-dimensional coordinate plane as follows.
00:00:21.880 --> 00:00:25.560
The unit vector 𝐢 hat corresponds to one unit in the 𝑥-direction.
00:00:26.080 --> 00:00:30.600
The unit vector 𝐣 hat corresponds to one unit in the positive 𝑦-direction.
00:00:30.960 --> 00:00:36.080
Finally, the unit vector 𝐤 hat corresponds to one unit in the positive 𝑧-direction.
00:00:36.080 --> 00:00:42.320
We can write any vector given in this form in terms of its Cartesian coordinates.
00:00:43.240 --> 00:00:46.560
This is written 𝑥, 𝑦, 𝑧 as shown.
00:00:47.240 --> 00:00:51.400
Vector 𝐀 is equal to nine 𝐢 plus three 𝐣 plus seven 𝐤.
00:00:51.800 --> 00:00:58.160
Therefore, our 𝑥-value is nine, the 𝑦-value is equal to three, and the 𝑧 or 𝑧-value is equal to seven.
00:00:58.600 --> 00:01:08.920
The vector 𝐀 nine 𝐢 plus three 𝐣 plus seven 𝐤 written in Cartesian coordinates is nine, three, seven.