Question Video: Geometric Applications of Vectors in a Square | Nagwa Question Video: Geometric Applications of Vectors in a Square | Nagwa

# Question Video: Geometric Applications of Vectors in a Square Mathematics • First Year of Secondary School

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If π΄π΅πΆπ· is a square and ππ + ππ = πππ, then π = οΌΏ. [A] 1 [B] 2 [C] 3 [D] 4

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### Video Transcript

If π΄π΅πΆπ· is a square and vector ππ plus vector ππ is equal to π multiplied by vector ππ, then π is equal to blank. Is it (A) one, (B) two, (C) three, or (D) four?

We recall that two vectors are equal if they have the same direction and magnitude. This means that when dealing with a square, the parallel sides will be represented by the same vectors as they have the same magnitude and direction. In this question, this means that vector ππ is equal to vector ππ and vector ππ is equal to vector ππ. The points π and π are the midpoints of the line segments π·πΆ and π΅πΆ, respectively. This means that the vector ππ is equal to the vector ππ and both of these are equal to a half of the vector ππ.

In the same way, vector ππ is equal to vector ππ, and these are equal to a half of vector ππ. In this question, we are told that vector ππ plus vector ππ is equal to π multiplied by vector ππ. We will begin by considering the two vectors on the left-hand side. We can see from the diagram that the vector ππ is equal to the vector ππ plus the vector ππ. We can also see that the vector ππ is equal to the vector ππ plus the vector ππ.

We know that the general vector ππ and the vector ππ are the additive inverse of one another. This means that they sum to give the zero vector. This also means that the vector ππ is equal to the negative of vector ππ. We know that vector ππ is equal to vector ππ and also that vector ππ is equal to a half of vector ππ. This means that vector ππ is equal to two multiplied by vector ππ. We also know that the vector ππ is equal to the vector ππ.

Our expression simplifies to two ππ plus ππ plus ππ plus ππ. ππ and ππ are the additive inverse of each other. Therefore, they sum to give a zero vector. We are therefore left with two ππ plus ππ, which gives us three multiplied by the vector ππ. This gives us the expression in the correct form such that π is equal to three. The correct answer is option (C).

If π΄π΅πΆπ· is a square and vector ππ plus vector ππ is equal to π multiplied by vector ππ, then π is equal to three.

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