Question

Starting from the point (-5,0,-4) reparametrize the curve

r(t)=(-5-3t)i+(0+2t)j+(-4-2t)k in terms of arclength.
r(t(s))=__i + __j + __k

Answer 1

To reparametrize the curve, find the position and velocity vectors, calculate the magnitude of the velocity vector, and use the formula r(t(s)) = r(t) / |v(t)|.

Step-by-step explanation:

To reparametrize the curve in terms of arc length, we need to find the position vector r(t) and the velocity vector v(t).

Given r(t) = (-5-3t)i + (0+2t)j + (-4-2t)k, we can find r'(t) by taking the derivative of each component: r'(t) = -3i + 2j - 2k.

Next, we need to find the magnitude of v(t): |v(t)| = sqrt((-3)^2 + (2)^2 + (-2)^2) = sqrt(17).

Finally, we can reparametrize the curve in terms of arc length using the formula r(t(s)) = r(t) / |v(t)|:

r(t(s)) = (-5-3t)sqrt(17)^-1 i + (0+2t)sqrt(17)^-1 j + (-4-2t)sqrt(17)^-1 k