# Math Help - curvature k(t) of the curve

1. ## curvature k(t) of the curve

Find the curvature $k(t)$ of the curve $X(t)= (-2 sin t) I + (-2 sin t)J + (1 cos t)K$
$k=\frac{|r' X r''|}{|r'|^3}$

$r(t) = (-2 sin t) I + (-2 sin t)J + (1 cos t)K$

$r'(t) = (-2 cos t) I + (-2 cos t)J + (- sin t)K$

$r''(t) = (2 sin t) I + (2 sin t)J + (-cos t)K$

Need help with the cross product, i'm not sure if im doing the cross product right but its:

$r' X r'' = (2 cos^2t)I - (2 cos^2t - 2 sin^2t) + (-4 cos t *sint -4 cos t *sin t)$