Print your name ---------------- SS# --*--*---

Show your work and give reasons for you answers on all of the following problems.
No calculators, books or notes are allowed.

1. Find a vector equation, parametric equations and symmetric equations for the line passing through the point P_o(-5,-3,-4) and parallel to the vector v = < 2,-5,-2 > .
2. Find a vector equation, parametric equations and symmetric equations for the line passing through the two points P(-1,-4,3) and Q(4,-1,-5).
3. Find a vector equation, parametric equations and symmetric equations for the line that passes through the point P_o(-3,-5,-2) and parallel to

   1. the line L₁ with parametric equations

      x = 3+(-2)t,   y = -5+(-5)t,   z = 2+(-3)t,    -¥ < t < ¥

   2. the line L₂ with vector equation

      r = < -3,-6,-4 > +t < 1,-6,2 > ,    -¥ < t < ¥

   3. the line L₃ with symmetric equations

      (x-(4))/1 = (y-(3))/-1 = (z-(-1))/2

4. Find an equation for the plane through the point P_o(5,3,-4) with a normal vector
   n = < 6,4,-3 > .
5. Find a vector equation, parametric equations and symmetric equations for the line that passes through the point P_o(5,0,-4) and is normal to the plane

   (-3)x +(-5)y +(4)z = 24

6. Find an equation for the plane passing through the point P_o(3,2,3 > and parallel to the plane

   (-3)x + (-3)y + (6)z = 0

7. Find an equation for the plane that passes through the point P_o(5,3,-5) and normal to the line L with parametric equations

   x = 2+(2)t,   y = 3+(-3)t,   z = 4+(2)t,    -¥ < t < ¥

8. Find an equation of the plane that passes through the points P(1,-2,3), Q(-2,5,-1) and R(1,-3,-4),
9. Determine whether the following line and plane are parallel. If they are not, find the point at which they intersect.

   x = 0+(-3)t,    y = 5+(4)t,    z = 3+(-5)t,       -¥ < t < ¥

   (-2)x+(1)y+(-4)z = -2

10. For section 11.6: Review sketches, problems done in class and problems on the exercise list. Add problems 39,40,43 and 44 to the exercise list.