### Video Transcript

The figure shows a regular hexagon π΄π΅πΆπ·πΈπΉ divided into six equilateral triangles. Which of the following is equal to ππ plus π
π? (A) ππ, (B) ππ, (C) π
π, (D) ππ, (E) ππ
.

Looking at our figure, we see this regular hexagon and the six equilateral triangles that make it up. We can recall that an equilateral triangle is one where all the side lengths are the same. That means, for example, that this side length, πΉπ΄, is the same as this length or this length or any such similar triangle side in this hexagon. In our question statement, weβre told about two vectors: vector ππ and vector π
π. On our figure, ππ looks like this, a vector from point π΅ to point πΈ. π
π is like this. Itβs half the length of ππ, and note that it points in the opposite direction.

That part about direction is important because it means when we go to add ππ and π
π, the result will look like this, a vector with the same length as π
π, but it points in the same direction as ππ. Note that to find this result, weβve effectively used the tip-to-tail method of vector addition. That is, weβve taken vector ππ then put the tail of vector π
π at the tip of ππ. And this shows us that the resultant of these two vectors, their vector sum, goes from the tail of ππ to the tip of π
π. This means that among our five answer options, weβre looking for the vector that looks like this one on our diagram. It will point straight upward like vector ππ, and it will have the same length or magnitude as vector π
π.

If we first look at option (A), vector ππ, that would look like this on our figure. It has the right magnitude but the wrong direction. Moving on to vector ππ, this vector also has the correct length or magnitude but the incorrect direction. Vector π
π in option (C) looks like this. This option is correct neither in direction nor magnitude. But then, if we look at vector ππ, this is the vector that goes from point πΆ to point π·. We see this has the same length as π
π, like we wanted, but it points upward like vector ππ. Vector ππ then is a match for our resultant vector. For completeness sake, letβs look at the last option vector ππ
. This vector also has the correct magnitude but the incorrect direction.

Of these answer options then, we find that itβs vector ππ thatβs equal to ππ plus π
π.