Video Transcript
Which of the vectors 𝐏, 𝐐, 𝐑,
𝐒, or 𝐓 shown in the diagram is equal to 𝐀 plus 𝐁?
So here we have a diagram showing
us seven vectors, including the vectors 𝐀 and 𝐁. And we’re being asked, of the other
five vectors 𝐏, 𝐐, 𝐑, 𝐒, and 𝐓, which one will be equal to the sum of 𝐀 and
𝐁. Since the vectors have been given
to us in a graphical form — they’re represented by the blue arrows — we can add them
together graphically using the tip-to-tail method. In the tip-to-tail method, one
vector slides over until its tail is on the tip of the other vector. The resultant is drawn from the
tail of the unmoved vector to the tip of the moved vector.
In our problem, we want to add
together the vectors 𝐀 and 𝐁. So let’s keep the vector 𝐀
stationary and slide the vector 𝐁 over so that its tail rests on the tip of vector
𝐀, making sure that both the horizontal and vertical components of vector 𝐁 as
we’ve drawn it now are the same as the original vector 𝐁. In this case, the horizontal
component is two units to the right and the vertical component is three units
upward. We can now draw on the resultant
vector, that is, the vector which is equivalent to 𝐀 plus 𝐁. This is drawn from the tail of the
unmoved vector 𝐀 to the tip of the moved vector 𝐁.
We can see that this resultant
vector has the same direction and magnitude as the vector 𝐐. In other words, it’s equal to
vector 𝐐. This means that vector 𝐐 is equal
to the sum of 𝐀 and 𝐁. Of the five vectors drawn in the
diagram, 𝐏, 𝐐, 𝐑, 𝐒, and 𝐓, it’s vector 𝐐 that’s equal to 𝐀 plus 𝐁.