WEBVTT
00:00:01.390 --> 00:00:17.970
Given that vector 𝐀 is equal to two, zero, two and vector 𝐁 is equal to zero, five, nine, express the vector 𝐀𝐁 in terms of the unit vectors 𝐢, 𝐣, and 𝐤.
00:00:19.500 --> 00:00:27.630
We begin by recalling that the vector 𝐀𝐁 is equal to the vector 𝐁 minus the vector 𝐀.
00:00:28.910 --> 00:00:37.260
In this question, we need to subtract the vector two, zero, two from the vector zero, five, nine.
00:00:38.300 --> 00:00:43.510
When subtracting vectors, we subtract the corresponding components.
00:00:44.320 --> 00:00:56.830
Zero minus two is equal to negative two, five minus zero is equal to five, and nine minus two is equal to seven.
00:00:57.910 --> 00:01:03.770
The vector 𝐀𝐁 has components negative two, five, and seven.
00:01:05.010 --> 00:01:17.490
We recall that the unit vectors 𝐢 hat, 𝐣 hat, and 𝐤 hat are vectors of magnitude one in the positive 𝑥-, 𝑦-, and 𝑧-directions.
00:01:18.570 --> 00:01:28.430
We have worked out that the 𝑥-component of our vector is negative two, the 𝑦-component is five, and the 𝑧-component is seven.
00:01:29.530 --> 00:01:42.300
This means that the vector 𝐀𝐁 written in terms of its unit vectors 𝐢, 𝐣, and 𝐤 is equal to negative two 𝐢 plus five 𝐣 plus seven 𝐤.