# Chapter 8 - Equations of Lines and Planes

Chapter 8.1 - Vector and Parametric Equations of a Line in R2

1. 2. 3. 4. 5. 6. 7. 8. 9.

Determine the point(s) where the line

r = (1,-5) + t(2,-1), t E R

intersects the curve 2y^2 + 20y - x + 47 = 0.

Chapter 8.2 - Cartesian Equation of a Line

10.

Determine the Cartesian equation for the line with a normal vector of (6,-5) passing through the point (2,1).

Answer:  6x-5y-7=0                                   Video Solution to #10

11.

A line passes through (7, -9) and (2,5).  Determine the Cartesian equation.

Answer:  14x + 5y - 53 = 0                  Video Solution to #11

12.

Determine a Cartesian equation for the line with the parametric equations x = 5 + t, y = -3t, t E R

Answer:  3x + y - 15 = 0             Video Solution to #12

13 abc 14.

The lines kx-2y+4 = 0 and 3x+y-12=0 have an angle of 45 degrees between them.  For what value(s) of k is this true?

Answer: k = 4, k = -1               Video Solution to #14

Chapter 8.3 - Vector, Parametric and Symmetric Equations of a Line in R3

15. 16.   empty question (for now)

17. 18. 19. 20. 21. 22. 23. 24abc. Chapter 8.4 - Vector and Parametric Equations of a Plane

25. 26. 27. 28. 29. 30. 31. Chapter 8.5 - The Cartesian Equation of a Plane

32.

Determine the Cartesian equation of the plane with normal vector (6, -1, 2) passing through the point (-1, 0, 4)

Answer:  6x - y + 2z - 2 = 0                          Video Solution to #32

33.

Determine three points on the plane 3x + 4y - 5z + 120 = 0

Answer:  (0, 0, 24), (0, -30, 0), and (14, -57, -13.2) among others.             Video Solution to #33

34.

Determine the vector and Cartesian equation of the plane containing the points (A(5,1,-2), B(-3,8,7) and C(-6,-5,-5).

Answer:  vector equation: r = (5, 1, -2) +s (8, -7, -9) + t (11,6,3), s, t ER

Cartesian equation:  33x - 123y + 125z + 208 = 0                    Video Solution to #34

35.

Determine the Cartesian equation of the plane that contains the origin and is perpendicular to the line containing the points A(7,-1,-4) and B(2,0,-5)

Answer:  5x - y + z = 0                               Video Solution to #35

36.

Determine the angle between the planes  3x-5y+2z-54 = 0  and  2x+y-8z+1= 0

Answer:  approx. 73.0 degrees or 107.0 degrees                  Video Solution to #36

37.

What value of k makes the planes  2x + y + kz - 17 = 0  and  7x - 2y + 2z + 11 = 0  perpendicular?

Answer: k = -6                         Video Solution to #37