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.
Answer: (5,-7) and (-1, -4)
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