Exercises In Exercises 1-8, write the equation of the plane with normal vector n passing through the given point in the scalar form ax + by + cz = d. 1. n = (1, 3, 2), (4, -1, 1) 2. n = (-1,2, 1), (3, 1,9) on 3. n = (-1, 2, 1), (4, 1,5) 4. n= (2, -4, 1), (3, 3,1) 5. n = i, (3, 1, -9) 6. n= j, (-5, 2, 2) a asab bas cozs ofr in one of 7. n = k, (6,7,2) 8. n=i-k, (4,2,-8) 9. Write the equation of any plane through the origin. 10. Write the equations of any two distinct planes with normal vector n = (3, 2, 1) that do not pass through the origin. 11. Which of the following statements are true of a plane that is parallel to the yz-plane? (a) n = (0, 0, 1) is a normal vector. (b) n = (1, 0, 0) is a normal vector. (c) The equation has the form ay + bz = d. (d) The equation has the form x = d. 12. Find a normal vector n and an equation for the planes in Figures 8 (A)-(C).lowing statements is correct? (a) L is contained in P. (b) L is orthogonal to P. -N -3 X X (A ) (B) (C) FIGURE 8 In Exercises 13-16, find a vector normal to the plane with the given equa- tion. 13. 9x - 4y - 11z = 2 14. x - z = 0 15. 3(x - 4) - 8(y - 1) + 11z = 0 16. x = 1 In Exercises 17-20, find the equation of the plane with the given descrip- tion. 17. Passes through O and is parallel to 4x - 9y + z = 3 18. Passes through (4, 1, 9) and is parallel to x + y + z = 3 19. Passes through (4, 1, 9) and is parallel to x = 3