1) Find an equation of the plane that passes through the point (8, 5, 1) and is parallel to the yz-plane.

2) Find a set of parametric equations of the line that passes through the point (1, 4, 5) and is parallel to v = 7i 4j.

(x(t), y(t), z(t)) =

3) The position vector r describes the path of an object moving in space. Find the velocity, speed, and acceleration of the object.r(t) = 7ti + 2tj + 6tk

v(t) = s(t) = a(t) =

4) Use the given acceleration function to find the velocity and position vectors. Then find the position at time t = 9. a(t) = 8i + 4k, v(0) = 8j, r(0) = 0

v(t)= , r(t)= , r(9)=

5) Find the unit tangent vector to the curve at the specified value of the parameter. (Give your answers correct to 3 decimal places.) r(t) = t³i + 3t²j, t = 4

6) Find T(t), N(t), a_T, and a_N at the given time t for the curve r(t). (Give your answers correct to 3 decimal places.) r(t) = t²i + 5tj, t = 2