Question Video: Properties of Vectors in the Shape of a Triangle Mathematics

Fill in the blank: In triangle π΄π΅πΆ, ππ + ππ = οΌΏ.

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Video Transcript

Fill in the blank: In triangle π΄π΅πΆ, the vector ππ plus the vector ππ is equal to what?

In this question, weβre looking at some geometric properties of vectors. So what weβre going to do is begin by sketching out triangle π΄π΅πΆ. Letβs suppose triangle π΄π΅πΆ look like this. The vector ππ takes us from point π΄ to point π΅ in a straight line. And so the vector ππ is the line denoted with the yellow arrow. Similarly, the vector ππ takes us from point π΅ to point πΆ in a straight line. So we denote the vector ππ 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 ππ takes us from π΄ to π΅ and the vector ππ takes us from π΅ to πΆ, the resultant is the complete journey that we take.

So letβs identify whatβs happened. We start at point π΄, we then move to point π΅ along vector ππ, and then we move along vector ππ to point πΆ. The resultant can be thought about as the movement that takes us from π΄ to πΆ. This time, thatβs the green arrow. Since we have a single straight line that takes us from π΄ to πΆ, we can say that the resultant of ππ and ππ is the vector ππ. And so in triangle π΄π΅πΆ, the vector ππ plus the vector ππ is the vector ππ.