Find the Curvature $K$ Of the Curve $\mathbf { r } ( t ) = \left( t , t , 1 - t ^ { 2 } \right)$

Multiple Choice

Find the curvature $K$ of the curve $\mathbf { r } ( t ) = \left( t , t , 1 - t ^ { 2 } \right)$ at t = 0.

A) 0
B) $\frac { 1 } { 8 }$
C) $\frac { 1 } { 4 }$
D) $\frac { 1 } { 2 }$
E) 1
F) 2
G) 4
H) 8