For the space curve

MATHEMATICS · Single correct · AP · Calculus BC · Parametric, Polar, and Vector-Valued Functions · Parametric, Polar, and Vector-Valued Functions

Problem

For the space curve

\mathbf r(t)=\langle\cos t,\sin t,t\rangle

, determine the equation of the normal plane at the point corresponding to

t=\pi/4

. (a)

\sqrt{2}\,x-\sqrt{2}\,y+2z=\dfrac{\pi}{2}

(b)

-\sqrt{2}\,x+\sqrt{2}\,y+2z=\dfrac{\pi}{2}

(c)

-\sqrt{2}\,x+\sqrt{2}\,y+z=\dfrac{\pi}{4}

(d)

-\sqrt{2}\,x+\sqrt{2}\,y+2z=\dfrac{\pi}{4}