### Video Transcript

Consider the given figure. If π΄π΅πΆπ· is a rectangle and πΈ is the midpoint of the line segment π΄π·, then vector ππ plus vector ππ minus vector ππ is equal to blank. Is it (A) vector ππ, (B) vector ππ, option (C) vector ππ, or option (D) vector ππ?

We begin by recalling that two vectors are equal if they have the same direction and magnitude. This means that in a rectangle, the parallel sides will be represented by the same vectors as they have the same magnitude and direction. This means that vector ππ is equal to vector ππ and vector ππ is equal to vector ππ. We are also told that πΈ is the midpoint of the line segment π΄π·. This means that vector ππ is equal to vector ππ, and both of these are equal to one-half multiplied by vector ππ.

Letβs now consider the expression we are given, vector ππ plus vector ππ minus vector ππ. We know that the general vectors ππ and ππ are the additive inverse of each other. This means that vector ππ plus vector ππ is equal to the zero vector. It also means that the vector ππ is equal to the negative of vector ππ. This means that instead of subtracting vector ππ, we can add vector ππ. Our expression can be rewritten as ππ plus ππ plus ππ.

From the diagram, we can see that the vector ππ can be rewritten as vector ππ plus vector ππ. This gives us the expression ππ plus ππ plus ππ plus ππ. As vector ππ and vector ππ are the additive inverse of one another, they will sum to give us the zero vector. So, we can therefore cancel these terms. As vector ππ is equal to vector ππ, then vector ππ will be equal to vector ππ. Our expression can be simplified to vector ππ plus vector ππ.

We can change the order of these two vectors so that the endpoint of the first vector is the start point of the second vector. We can see from the diagram that the vector ππ plus the vector ππ is equivalent to the vector ππ. The correct answer is therefore option (B).

If π΄π΅πΆπ· is a rectangle and πΈ is the midpoint of line segment π΄π·, then the vector ππ plus the vector ππ minus the vector ππ is equal to the vector ππ.