Video Transcript
Which of the vectors 𝐏, 𝐐, 𝐑, 𝐒, or 𝐓 shown in the diagram is equal to 𝚨 plus 𝚩?
The diagram is this set of Cartesian axes with several vectors represented as arrows. And we’re asked to identify which of those vectors is equal to the sum of the vectors 𝚨 and 𝚩, where 𝚨 and 𝚩 are represented by this arrow here and this arrow here. We recall that a vector represented by an arrow has a tail and a head. And when we draw the tail of one arrow at the head of another arrow, the arrow that connects the remaining tail to the remaining head gives us the sum of those two vectors. So to find 𝚨 plus 𝚩, we need to redraw the arrow’s tail to head and then find which of the other arrows has its tail at the remaining tail and its head at the remaining head.
Now, vector addition is commutative, so 𝚨 plus 𝚩 is equal to 𝚩 plus 𝚨. So let’s draw both of the possibilities, 𝚩 at the head of 𝚨 and 𝚨 at the head of 𝚩, just to make sure that our answer is consistent. The arrow representing 𝚨 extends one unit to the right and four units downward. And here is that same arrow with its tail at the head of 𝚩. Now 𝚩 extends four units to the right and one unit downward. And here is that arrow drawn from the head of vector 𝚨. Whichever way we draw these arrows, the remaining tail is at the origin where the tail of all the vectors are, and the remaining head is at this point here, the same location as the head of the vector 𝐐. So 𝐐 is the vector whose tail is at the remaining tail and whose head is at the remaining head. So 𝐐 is the vector that is equal to 𝚨 plus 𝚩.
