For the curve r(t), find an equation for the indicated plane at the given value of t.
-r(t) = (cosh t)i + (sinh t)j + tk; rectifying plane at t = 0.
A) x - y = -1
B) x - y = 1
C) x = 1
D) x = -1

Question

Quizplus · Accepted Answer

The rectifying plane at t=0 is perpendicular to the tangent vector at that point, which is the derivative of r(t) evaluated at t=0. We have:

r'(t) = sinh(t)i + cosh(t)j + k

So, at t=0, we have r'(0) = j + k. The plane perpendicular to this vector passing through the point r(0) = i is given by the equation x = 1. Therefore, the correct choice is C.

For the Curve R(t), Find an Equation for the Indicated