Find the magnitude and direction of the vector represented by the following pairs of components:
(a) Ax = -8.60 cm, Ay = 5.20 cm; (b) Ax = -9.70 m., Ay = -2.45 m; (c) Ax = 7.75 km, Ay = -2.70 km.
(a) A=Ax2+Ay2=10 cm,θ=arctan(Ax/Ay)=149°.A=\sqrt{A_x^2+A_y^2}=10\text{ cm},\theta=\arctan(A_x/A_y)=149°.A=Ax2+Ay2=10 cm,θ=arctan(Ax/Ay)=149°.
(b) A=Ax2+Ay2=10 cm,θ=arctan(Ax/Ay)=194°.A=\sqrt{A_x^2+A_y^2}=10\text{ cm},\theta=\arctan(A_x/A_y)=194°.A=Ax2+Ay2=10 cm,θ=arctan(Ax/Ay)=194°.
(c) A=Ax2+Ay2=8.2 cm,θ=arctan(Ay/Ax)=−19°.A=\sqrt{A_x^2+A_y^2}=8.2\text{ cm},\theta=\arctan(A_y/A_x)=-19°.A=Ax2+Ay2=8.2 cm,θ=arctan(Ay/Ax)=−19°.
All angles are from positive x-axis.
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