Find a vector equation for the line through the point $P = (1, ? 1, 0)$ and parallel to the vector $v = 2 i + 1 j ? 2 k$ . Assume $r (0) = 1 i ? 1 j + 0 k$ and that $v$ is the velocity vector of the line.. $r i (t) = j + k$ Find the curvature $? (t)$ of the curve $r (t) = (5 sin t) i + (5 sin t) j + (? 5 cos t) k$ $? (t) =$ The position function of a particle is given by $r (t) = ? 3 t^{2}, 5 t, t^{2} ? 4 t ?$ . At what time is the speed of the particle at a minimum? $t =$

Question

Find a vector equation for the line through the point

P = (1, ? 1, 0)

and parallel to the vector

v = 2 i + 1 j ? 2 k

. Assume

r (0) = 1 i ? 1 j + 0 k

and that

v

is the velocity vector of the line..

r i (t) = j + k

Find the curvature

? (t)

of the curve

r (t) = (5 sin t) i + (5 sin t) j + (? 5 cos t) k

? (t) =

The position function of a particle is given by

r (t) = ? 3 t^{2}, 5 t, t^{2} ? 4 t ?

. At what time is the speed of the particle at a minimum?

t =

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