WEBVTT
00:00:01.410 --> 00:00:08.620
When is it true that vector 𝐮 plus vector 𝐯 is equal to vector 𝐯 plus vector 𝐮?
00:00:10.170 --> 00:00:14.630
Is it (A) only when vectors 𝐮 and 𝐯 are equivalent?
00:00:15.170 --> 00:00:19.490
(B) Only when vectors 𝐮 and 𝐯 are parallel.
00:00:20.190 --> 00:00:24.600
(C) Only when vectors 𝐮 and 𝐯 are perpendicular.
00:00:25.370 --> 00:00:30.270
(D) Only when vectors 𝐮 and 𝐯 are not perpendicular.
00:00:30.880 --> 00:00:34.860
Or (E) for any vectors 𝐮 and 𝐯.
00:00:36.310 --> 00:00:44.830
Let’s begin by letting vector 𝐮 have components 𝑥 one, 𝑦 one and vector 𝐯 have components 𝑥 two, 𝑦 two.
00:00:46.080 --> 00:00:51.070
We know that when adding vectors, we simply add the corresponding components.
00:00:51.290 --> 00:00:58.940
Therefore, vector 𝐮 plus vector 𝐯 has components 𝑥 one plus 𝑥 two and 𝑦 one plus 𝑦 two.
00:01:00.160 --> 00:01:08.250
In the same way, vector 𝐯 plus vector 𝐮 has components 𝑥 two plus 𝑥 one and 𝑦 two plus 𝑦 one.
00:01:09.260 --> 00:01:18.970
We know that the values of 𝑥 one, 𝑥 two, 𝑦 one, and 𝑦 two are all scalars and that adding two scalars is commutative.
00:01:20.080 --> 00:01:26.270
This means that 𝑥 one plus 𝑥 two will give us the same value as 𝑥 two plus 𝑥 one.
00:01:27.100 --> 00:01:33.420
Likewise, 𝑦 one plus 𝑦 two gives the same value as 𝑦 two plus 𝑦 one.
00:01:34.430 --> 00:01:37.590
This means that the correct answer is option (E).
00:01:38.010 --> 00:01:45.970
Vector 𝐮 plus vector 𝐯 is equal to vector 𝐯 plus vector 𝐮 for any vectors 𝐮 and 𝐯.
00:01:47.110 --> 00:01:52.540
This leads us to a general rule that the addition of vectors is commutative.