# Question Video: Understanding Vectors Between Two Given Points Mathematics

Which of the following is equal to the vector 𝐀𝐁? [A] 𝐀 + 𝐁 [B] 𝐀 − 𝐁 [C] 𝐁 − 𝐀 [D] 𝐀 × 𝐁

01:25

### Video Transcript

Which of the following is equal to the vector 𝐀𝐁? Is it (A) 𝐀 plus 𝐁, (B) 𝐀 minus 𝐁, (C) 𝐁 minus 𝐀, or (D) 𝐀 times 𝐁?

Let’s begin by considering the two points 𝐴 and 𝐵 on a two-dimensional coordinate grid. The vector 𝐀 will take us from the origin 𝑂 to the point 𝐴. Likewise, vector 𝐁 will take us from the origin to the point 𝐵. We need to work out how we can get from point 𝐴 to point 𝐵. One way of doing this is going via the origin 𝑂. This means that vector 𝐀𝐁 is equal to vector 𝐀𝐎 plus vector 𝐎𝐁. As the vector 𝐎𝐀 equals 𝐀, then the vector 𝐀𝐎 will be negative 𝐀, as it is going in the opposite direction but has the same magnitude. The vector 𝐎𝐁 is equal to 𝐁. Negative 𝐀 plus 𝐁 can be rewritten as 𝐁 minus 𝐀. This means that the correct answer is option (C). The vector 𝐀𝐁 is equal to vector 𝐁 minus vector 𝐀.

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