Find the magnitude and direction of the following vector represented by the following pairs of components
a) Ax=8.60cm. Ay=5.20cm
b) Ax=9.70m. Ay=2.45m
c) Ax= 7.75km. Ay=2.70km
1
Expert's answer
2019-05-27T11:09:37-0400
a) We can find the magnitude of the vector A from the formula:
A=∣A∣=Ax2+Ay2=(8.60cm)2+(5.20cm)2=10cm.
We can find the angle between the vector A and the +x-axis from the formula:
θ=arctan(AxAy)=arctan(8.60cm5.20cm)=31∘.
b) We can find the magnitude of the vector A from the formula:
A=∣A∣=Ax2+Ay2=(9.70m)2+(2.45m)2=10m.
We can find the angle between the vector A and the +x-axis from the formula:
θ=arctan(AxAy)=arctan(9.70m2.45m)=14∘.
c) We can find the magnitude of the vector A from the formula:
A=∣A∣=Ax2+Ay2=(7.75km)2+(2.70km)2=8.21km.
We can find the angle between the vector A and the +x-axis from the formula:
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