Question

find angle between 2N and 3N forces if their resultant is 4N

Answer 1

Heya.......!!!

Resultant of two Vectors is
$\sqrt{a {}^{2} + b {}^{2} + 2ab \cos( \alpha ) } \\ \\ here \: a \: and \: b \: are \: two \: vectors \: \\ \: \alpha \: is \: the \: angle \: between \: them \: \: \\ \\ now \: putting \: the \: values \: in \: th e \: formulae \: \: we \: get \: \\ \\ \: \: \: \sqrt{2 {}^{2} + 3 {}^{2} + 2 \times 2 \times 3 \cos( \alpha ) } = 4 \: \\ squaring \: both \: the \: sides \: we \: get \: \\ \\ 13 + 12 \cos( \alpha ) = 16 \\ 12 \cos( \alpha ) = 3 \\ \cos( \alpha ) = 3 \div 12 \\ \cos( \alpha )= 1 \div 4 \\ \alpha = \cos( {}^{ - 1}) \frac{1}{4}$


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