3. This one is tougher! Consider y' the vector A in the figure to the right, making an angle 0 with re- spect to the x and y axes. that, if the length of the vector is = A, the components in this co- ordinate system are given by Show Ay O А, A cos e A sin 0 Ax Now, suppose you rotate the coordinate system by an angle d, so that the vector now makes an angle a with respect to the x' and y' axes. Show that the new components can be written in terms of the old ones as A cos A, sin d = -A, sin 0 + A cos ). A4 A A. That is, the length of the arrow Finally, show that the length of the vector doesn't change if we turn our heads and look at it sideways.

3. This one is tougher! Consider y' the vector A in the figure to the right, making an angle 0 with re- spect to the x and y axes. that, if the length of the vector is = A, the components in this co- ordinate system are given by Show Ay O А, A cos e A sin 0 Ax Now, suppose you rotate the coordinate system by an angle d, so that the vector now makes an angle a with respect to the x' and y' axes. Show that the new components can be written in terms of the old ones as A cos A, sin d = -A, sin 0 + A cos ). A4 A A. That is, the length of the arrow Finally, show that the length of the vector doesn't change if we turn our heads and look at it sideways.

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Question

100%

3. This one is tougher! Consider y'
the vector A in the figure to the
right, making an angle 0 with re-
spect to the x and y axes.
that, if the length of the vector is
= A, the components in this co-
ordinate system are given by
Show
Ay
O
А,
A cos e
A sin 0
Ax
Now, suppose you rotate the coordinate system by an angle d, so that the vector now
makes an angle a with respect to the x' and y' axes. Show that the new components
can be written in terms of the old ones as
A cos A, sin d
= -A, sin 0 + A cos ).
A4
A
A. That is, the length of the arrow
Finally, show that the length of the vector
doesn't change if we turn our heads and look at it sideways.

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