Question #246751

If C = [2.5 cm, 80°], i.e., the magnitude and direction of C are 2.5 cm and 80°, D = [3.5 cm,

120°], and E = D – 2C, then what is the direction of E (to the nearest degree)?

 


1
Expert's answer
2021-10-06T10:05:25-0400
c=(2.5cos80°,2.5sin80°)\vec c=(2.5\cos 80\degree, 2.5\sin 80\degree)

d=(3.5cos120°,3.5sin120°)\vec d=(3.5\cos 120\degree, 3.5\sin 120\degree)

e=d2c=(3.5cos120°,3.5sin120°)\vec e=\vec d-2\vec c=(3.5\cos 120\degree, 3.5\sin 120\degree)

2(2.5cos80°,2.5sin80°)-2(2.5\cos 80\degree, 2.5\sin 80\degree)

=(3.5cos120°5cos80°,3.5sin120°5sin80°)=(3.5\cos 120\degree-5\cos 80\degree, 3.5\sin 120\degree-5\sin 80\degree)

tanθ=3.5sin120°5sin80°3.5cos120°5cos80°\tan \theta=\dfrac{3.5\sin 120\degree-5\sin 80\degree}{3.5\cos 120\degree-5\cos 80\degree}

θ=tan1(3.5sin120°5sin80°3.5cos120°5cos80°)\theta=\tan^{-1}(\dfrac{3.5\sin 120\degree-5\sin 80\degree}{3.5\cos 120\degree-5\cos 80\degree})

36°\approx36\degree


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