?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]

Unfortunately, we don't have that question answered yet. But you can get it answered in just 5 hours by Logging in or Becoming a subscriber.

Becoming a subscriber
Or look for another answer

×

Login

Login or Sign up for access to all of our study tools and educational content!

Forgot password?
Register Now

×

Register

Sign up for access to all content on our site!

Or login if you already have an account

×

Reset password

If you have an active account we’ll send you an e-mail for password recovery

Or login if you have your password back