দুটি ভেক্টর $\overrightarrow{A}$ এবং $\overrightarrow{B}$ -এর যোগফল তাদের পার্থক্যের ওপর লম্ব। নিচের কোন বিবৃতিটি অবশ্যই সত্য? (The sum of two vectors $\overrightarrow{A}$ and $\overrightarrow{B}$ is perpendicular to their difference. Which one of the following statements must be true?)

The statement that the answer given is correct can be explained using properties of vectors in geometry.

When the sum of two vectors $\overrightarrow{A}$ and $\overrightarrow{B}$ is perpendicular to their difference, it means that the two vectors are oriented in such a way that they form a right angle with respect to one another at that point.

If we denote the sum of the vectors as $\overrightarrow{S}$ and the difference as $\overrightarrow{D}$, we can say:

    
1. $\overrightarrow{S}$ = $\overrightarrow{A}$ + $\overrightarrow{B}$
    
2. $\overrightarrow{D}$ = $\overrightarrow{A}$ - $\overrightarrow{B}$

For the sum $\overrightarrow{S}$ to be perpendicular to the difference $\overrightarrow{D}$, the dot product of these two vectors must equal zero:

Now, among the provided options, the first option states that the magnitudes of the vectors A and B are equal:

This equality suggests that both vectors have the same length, which can lead to the scenario where their sum is perpendicular to their difference. Therefore, this statement must be true under the given conditions.

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