Question

The resultant of F and 2F is under root 3F Then find the angle between these forces?


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Answer 1

$\huge\mathfrak\red{Answer}$

$let \: a \: and \: be \: are \: the \: two \: vector \\ with \: angle \: \alpha \: btween \: them \\ \\ then \: resultant \: of \: these \: two \\ vector \: will \: be \\ \\ { |r| }^{2} = { |a| }^{2} + { |b| }^{2} + 2 |a| |b| \cos \alpha \\ \\ where \: r \: is \: the \: resultant \: of \: the \: vector$

ANSWER

${(3f)}^{2} = {f}^{2} + {(2f)}^{2} + 2(f)(2f) \cos \alpha \\ \\ 9 {f}^{2} = {f}^{2} + 4 {f}^{2} + 4 {f}^{2} \cos \alpha \\ \\ 9 {f}^{2} = 5 {f}^{2} + 4 {f}^{2} \cos \alpha \\ \\ 4 {f}^{2} = 4 {f}^{2} \cos \alpha \\ \\ \cos \alpha = 1 \\ \\ \alpha = 0$