?Consider vector \(\mathbf{a}(x)=\left\langle x, \sqrt{1-x^{2}}\right\rangle\) with
Chapter 2, Problem 22(choose chapter or problem)
Consider vector \(\mathbf{a}(x)=\left\langle x, \sqrt{1-x^{2}}\right\rangle\) with components that depend on a real number \(x \in[-1,1]\). As the number x varies, the components of a(x) change as well, depending on the functions that define them.
a. Write the vectors a(0) and a(1) in component form.
b. Show that the magnitude ‖ a(x) ‖ of vector a(x) remains constant for any real number x
c. As x varies, show that the terminal point of vector a(x) describes a circle centered at the origin of radius 1.
Text Transcription:
a(x) = langle x, sqrt 1-x^2 rangle
x in[-1,1]
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