The tangent line to a smooth curve r t f t l g t h t k at t to is the line that passes through the point to 9 to h t parallel to v to the curve s velocity vector at to User to and r to to find parametric equations for the line that is tangent to the given curve at the given parameter value t to r t cos t i 3 sin t j 3 k o 0 Find the standard parametrization for the tangent line OA x 1 y 3t z 3 9t OB x 1 y 2t 3 z 3 c x 0 y 3t z 3 9t D x 0 y 2t 3 z 3 CIES