Question Video: Understanding Vectors Between Two Given Points Mathematics

Which of the following is equal to the vector 𝐀𝐁? [A] 𝐀 + 𝐁 [B] 𝐀 βˆ’ 𝐁 [C] 𝐁 βˆ’ 𝐀 [D] 𝐀 Γ— 𝐁

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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 𝐡 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 𝐡. We need to work out how we can get from point 𝐴 to point 𝐡. One way of doing this is going via the origin 𝑂. This means that vector 𝐀𝐁 is equal to vector π€πŽ plus vector 𝐎𝐁. As the vector πŽπ€ equals 𝐀, then the vector π€πŽ 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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