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Given-that-forces-F-1-and-F-2-position-vectors-r-1-and-r-2-F-1-2i-3j-N-r-1-i-2j-F-2-i-7j-N-r-2-3i-4j-Given-that-these-system-of-forces-form-a-couple-f




Question Number 87754 by Rio Michael last updated on 06/Apr/20
Given that forces F_(1 )  and F_2  position vectors r_(1 ) and r_2     F_1  = (2i + 3j)N        r_1 = i + 2j     F_2  = (αi−7j) N        r_2  = 3i + 4j  Given that these system of forces form a couple   find the value of α.
$$\mathrm{Given}\:\mathrm{that}\:\mathrm{forces}\:\mathrm{F}_{\mathrm{1}\:} \:\mathrm{and}\:\mathrm{F}_{\mathrm{2}} \:\mathrm{position}\:\mathrm{vectors}\:\mathrm{r}_{\mathrm{1}\:} \mathrm{and}\:\mathrm{r}_{\mathrm{2}} \\ $$$$\:\:\boldsymbol{\mathrm{F}}_{\mathrm{1}} \:=\:\left(\mathrm{2}\boldsymbol{{i}}\:+\:\mathrm{3}\boldsymbol{{j}}\right)\mathrm{N}\:\:\:\:\:\:\:\:\boldsymbol{\mathrm{r}}_{\mathrm{1}} =\:\boldsymbol{\mathrm{i}}\:+\:\mathrm{2}\boldsymbol{\mathrm{j}} \\ $$$$\:\:\:\boldsymbol{\mathrm{F}}_{\mathrm{2}} \:=\:\left(\alpha\boldsymbol{{i}}−\mathrm{7}\boldsymbol{{j}}\right)\:\mathrm{N}\:\:\:\:\:\:\:\:\boldsymbol{\mathrm{r}}_{\mathrm{2}} \:=\:\mathrm{3}\boldsymbol{\mathrm{i}}\:+\:\mathrm{4}\boldsymbol{\mathrm{j}} \\ $$$$\mathrm{Given}\:\mathrm{that}\:\mathrm{these}\:\mathrm{system}\:\mathrm{of}\:\mathrm{forces}\:\mathrm{form}\:\mathrm{a}\:\mathrm{couple} \\ $$$$\:\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\alpha. \\ $$

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