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.