Video: Finding the Unknown Forces of Three Coplanar Force Vectors in Equilibrium

Given that ๐นโ‚, ๐นโ‚‚ and ๐นโ‚ƒ are three coplanar forces in equilibrium meeting at a point, where ๐นโ‚ = 5๐‘– โˆ’ 3๐‘— and ๐นโ‚‚ = 4๐‘– โˆ’ 14๐‘—, find ๐นโ‚ƒ.

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Video Transcript

Given that ๐น one, ๐น two, and ๐น three are three coplanar forces in equilibrium meeting at a point where ๐น one equals five ๐‘– minus three ๐‘— and ๐น two equals four ๐‘– minus 14๐‘—, find ๐น three.

As the three forces are in equilibrium, ๐น one plus ๐น two plus ๐น three must be equal to zero ๐‘– plus zero ๐‘—. Substituting in the values of force, ๐น one and ๐น two, gives us five ๐‘– minus three ๐‘— plus four ๐‘– minus 14๐‘— plus ๐น three equals zero ๐‘– plus zero ๐‘—.

Grouping the like terms on the left-hand side gives us nine ๐‘– minus 17๐‘— plus ๐น three is equal to zero ๐‘– plus zero ๐‘—, as five ๐‘– plus four ๐‘– is equal to nine ๐‘– and negative three ๐‘— minus 14๐‘— is negative 17๐‘—.

Balancing this equation by subtracting nine ๐‘– and adding 17๐‘— to both sides of the equation gives us ๐น three is equal to negative nine ๐‘– plus 17๐‘—. This means that, in order for the three coplanar forces to be in equilibrium, where ๐น one equals five ๐‘– minus three ๐‘— and ๐น two equals four ๐‘– minus 14๐‘—, then ๐น three must be equal to negative nine ๐‘– plus 17๐‘—.

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