Question

consider the circle r(t)= (a cos t, a sin t), for 0≤ t ≤ 2pi, where a is a positive real number, compute r' and show that it is orthogonal to r for all t.

Answer 1

\[r(t)= (a\cos t, a\sin t)\]\[r'(t)= (-a\sin t, a\cos t)\]\[r(t)\cdot r'(t)=-a^2\sin t\cos t+a^2\sin t\cos t=0\]

Answer 2

does the third step show that its orthogonal?

Answer 3

\[\hat{u}\cdot\hat{v}=|\hat{u}||\hat{v}|\cos\angle{(\hat{u},\hat{v})}=0\quad\Rightarrow\quad\hat{u}\perp\hat{v}\]

Answer 4

yea thats what i was thinking since it has to be right triangle to be orhoganol

Answer 5

thanks