### Video Transcript

Fill in the blank: In triangle π΄π΅πΆ, the vector ππ plus the vector ππ is equal to what?

In this question, weβre looking at some geometric properties of vectors. So what weβre going to do is begin by sketching out triangle π΄π΅πΆ. Letβs suppose triangle π΄π΅πΆ look like this. The vector ππ takes us from point π΄ to point π΅ in a straight line. And so the vector ππ is the line denoted with the yellow arrow. Similarly, the vector ππ takes us from point π΅ to point πΆ in a straight line. So we denote the vector ππ with the pink arrow. Then the sum of these two vectors is said to be its resultant. If we think about each vector as a journey, the vector ππ takes us from π΄ to π΅ and the vector ππ takes us from π΅ to πΆ, the resultant is the complete journey that we take.

So letβs identify whatβs happened. We start at point π΄, we then move to point π΅ along vector ππ, and then we move along vector ππ to point πΆ. The resultant can be thought about as the movement that takes us from π΄ to πΆ. This time, thatβs the green arrow. Since we have a single straight line that takes us from π΄ to πΆ, we can say that the resultant of ππ and ππ is the vector ππ. And so in triangle π΄π΅πΆ, the vector ππ plus the vector ππ is the vector ππ.