The point on the curve at which the tangent vector is parallel to the radius vector is

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

Problem

The point

P

on the curve

r(t) = (1 - 2t)\hat{i} + t^2\hat{j} + 2e^{2(t-1)}\hat{k}

at which the tangent vector

r'(t)

is parallel to the radius vector

r(t)

is (1)

(-1, 1, 2)

(2)

(1, -1, 2)

(3)

(-1, 1, -2)

(4)

(1, 1, 2)