Video Transcript
Given that 𝐅 sub one and 𝐅 sub two are two forces which form a couple, where 𝐅 sub one is equal to negative eight 𝐢 minus 𝐣, determine 𝐅 sub two.
We begin by recalling that a couple is a pair of parallel forces with equal magnitude and opposite direction which do not lie on the same line of action. If 𝐅 sub one and 𝐅 sub two are two forces which form a couple, then 𝐅 sub one plus 𝐅 sub two is equal to the zero vector. This means that 𝐅 sub two that we are trying to calculate in this question is equal to negative 𝐅 sub one. And since 𝐅 sub one is equal to negative eight 𝐢 minus 𝐣, then 𝐅 sub two is equal to negative negative eight 𝐢 minus 𝐣. Distributing negative one across our parentheses gives us eight 𝐢 plus 𝐣.
The force 𝐅 sub two which forms a couple with negative eight 𝐢 minus 𝐣 is eight 𝐢 plus 𝐣.
