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.

University Physics Volume 1

18th Edition

ISBN:9781938168277

Author:William Moebs, Samuel J. Ling, Jeff Sanny

Publisher:William Moebs, Samuel J. Ling, Jeff Sanny

Chapter2: Vectors

Section: Chapter Questions

Problem 2.10CYU: Check Your Understanding Verify that vector v V obtained in Example 2.14 is indeed a unit vector by...

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