Question

F1=150N F2=80N F3=110N F4=100N

Find the dot product 150N•80N and 110N•100N using magnitudes
Find the dot product 150N•110N and 80N•100N using components
Find the cross product 150N x 80N and 110N x 100N using magnitudes
Find the cross product 150N x 100N and 80N x 110N using components

Answer 1

Answer on Question #71547-Physics-Other

F1=150N F2=80N F3=110N F4=100N

Solution

Find the dot product 150N•80N and 110N•100N using magnitudes

$$(150)(80)\ \cos(90 - 30 + 20) = 2084$$ $$(110)(100)\ \cos(90 - 15) = 2847$$

Find the dot product 150N•110N and 80N•100N using components

$$150\ \cos 30\ (-80\ \sin 20) + 150\ \sin 30\ (80\ \cos 20) = 2084$$ $$100\ \cos 15\ (0) - 100\ \sin 15\ (-110) = 2847$$

Find the cross product 150N x 80N and 110N x 100N using magnitudes

$$(150)(80)\ \sin(90 - 30 + 20) = 11818$$ $$(110)(100)\ \sin(90 - 15) = 10625$$

Find the cross product 150N x 100N and 80N x 110N using components

$$\left| \begin{array}{cc} 150\ \cos 30 & 150\ \sin 30 \\ -80\ \sin 20 & 80\ \cos 20 \end{array} \right| = 150\ \cos 30\ (80\ \cos 20) - 150\ \sin 30\ (-80\ \sin 20) = 11818$$ $$\left| \begin{array}{cc} 0 & -110 \\ 100\ \cos 15 & -100\ \sin 15 \end{array} \right| = -100\ \sin 15\ (0) - 100\ \cos 15\ (-110) = 10625$$

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