Question Video: Subtracting Vectors Mathematics

Video Transcript

If vector 𝐀 is equal to negative five 𝐢 minus eight 𝐣 plus six 𝐤 and vector 𝐁 is equal to four 𝐢 minus three 𝐣 plus 13𝐤, find vector 𝐀 minus vector 𝐁.

We recall that in order to subtract two vectors, we simply subtract their corresponding components. In this question, we need to subtract the vector four 𝐢 minus three 𝐣 plus 13𝐤 from the vector negative five 𝐢 minus eight 𝐣 plus six 𝐤. We begin by considering the 𝐢-components. We have negative five 𝐢 minus four 𝐢. This is equal to negative nine 𝐢. Next, we have the 𝐣-components, negative eight 𝐣 minus negative three 𝐣. This is the same as negative eight 𝐣 plus three 𝐣, which simplifies to negative five 𝐣. Finally, with the 𝐤-components, we need to subtract 13𝐤 from six 𝐤. This is equal to negative seven 𝐤.

If vector 𝐀 is equal to negative five 𝐢 minus eight 𝐣 plus six 𝐤 and vector 𝐁 is equal to four 𝐢 minus three 𝐣 plus 13𝐤, then 𝐀 minus 𝐁 is equal to negative nine 𝐢 minus five 𝐣 minus seven 𝐤. These vectors could also have been written in terms of their 𝐢, 𝐣, and 𝐤 unit vector components. This can be done using triangular brackets as shown.