1. A line passes through the points A(2, 3) and B(-2, 1). Find a vector equation of the line. [x, y] = [-4, -2] + 42, 3] [x, y) = [2, 3] + 1-4,-2] [x, y] = [2, 3] + (-2, 1) [x, y] = [-2, 1] + (2, 3] A B D 2. A line has slope -3 and y-intercept 5. Find a vector equation of the line. [x, y] = [0, 5] + 11, -3] [x, y] = [1, -3] + 10, 5J Ix, yl =1-3, 5j + i-3, -31 A B [x, y] = [5, 0] + rſ0, –31 D _ 3. The Cartesian cquation of the plane with normal veetor i = [1, 2, 1] and passing through the point (3, 2, 1) is: x+ 2y + z+ 8 = 0 B x+ 2y +z- 8 = 0 3x + 2y +z- 8 = 0 3x + 2y +z+ 8 - 0 _ 4. The equation of a plane is [x, y, z] – [3, 1, 3] + s[=1, 1, 2] + f[2, 1, 1). Find a normal vector to the plane. [3, 1, 3] [-1, 5, –3] [-1, 1, 2] [2, 1, 1] A В D 5. The equation of a plane is x+ 2y + 3z- 6 = 0 . Find the y-intereept of the plane. D -3 _ 6. Two planes are parallel if their normals are perpendicular are collinear dot product is zero are different A B 7. Which of the following determines a plane? A a line and a point not on the line B two intersecting lines C two parallel, non-coincident lines D all of the above 8. Which of the following is not a plane? - -(1,3,4) + 3(2,-1,2) + +(1, 1,1), 5,t e R B 7- (2,4,2) + 5(1,-2, 3) + :(3,2,2), 5,t e R 7 - (3,2,3) + <(4,-4,2) + *(-2,2,-1). 5, e R D 7-(-2,1,4) + :(2,2-1)+-(2,2,1). s,t e R х+2 у-1 9. Which of the following points is not on the line ** . A P(7,7,12) B P(-2,1,3) C P(-11,-5,-6) D none of the above 10. On which of the following planes could the point P(0, 4, 3) lie? A x-3 В у-3 C z-3 none of the above D.
1. A line passes through the points A(2, 3) and B(-2, 1). Find a vector equation of the line. [x, y] = [-4, -2] + 42, 3] [x, y) = [2, 3] + 1-4,-2] [x, y] = [2, 3] + (-2, 1) [x, y] = [-2, 1] + (2, 3] A B D 2. A line has slope -3 and y-intercept 5. Find a vector equation of the line. [x, y] = [0, 5] + 11, -3] [x, y] = [1, -3] + 10, 5J Ix, yl =1-3, 5j + i-3, -31 A B [x, y] = [5, 0] + rſ0, –31 D _ 3. The Cartesian cquation of the plane with normal veetor i = [1, 2, 1] and passing through the point (3, 2, 1) is: x+ 2y + z+ 8 = 0 B x+ 2y +z- 8 = 0 3x + 2y +z- 8 = 0 3x + 2y +z+ 8 - 0 _ 4. The equation of a plane is [x, y, z] – [3, 1, 3] + s[=1, 1, 2] + f[2, 1, 1). Find a normal vector to the plane. [3, 1, 3] [-1, 5, –3] [-1, 1, 2] [2, 1, 1] A В D 5. The equation of a plane is x+ 2y + 3z- 6 = 0 . Find the y-intereept of the plane. D -3 _ 6. Two planes are parallel if their normals are perpendicular are collinear dot product is zero are different A B 7. Which of the following determines a plane? A a line and a point not on the line B two intersecting lines C two parallel, non-coincident lines D all of the above 8. Which of the following is not a plane? - -(1,3,4) + 3(2,-1,2) + +(1, 1,1), 5,t e R B 7- (2,4,2) + 5(1,-2, 3) + :(3,2,2), 5,t e R 7 - (3,2,3) + <(4,-4,2) + *(-2,2,-1). 5, e R D 7-(-2,1,4) + :(2,2-1)+-(2,2,1). s,t e R х+2 у-1 9. Which of the following points is not on the line ** . A P(7,7,12) B P(-2,1,3) C P(-11,-5,-6) D none of the above 10. On which of the following planes could the point P(0, 4, 3) lie? A x-3 В у-3 C z-3 none of the above D.
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter1: Vectors
Section1.3: Lines And Planes
Problem 18EQ
Related questions
Question
![1. A line passes through the points A(2, 3) and B(-2, 1). Find a vector equation of the line.
[x, y] = [-4, -2] + 12, 3]
[x, yl = [2, 3] + 41-4,-2]
[x, y) = [2, 3] + 1-2, 1]
A
В
D
2. A line has slope 3 and y-intereept 5. Find a vector equation of the line.
[x, y] = [1, -3] + [0, 5)
[x, yl =[-3, 5] + -3, -31
[x, y] = [0, 5] + [1, –3]
[x, yl - [5, 0j + j0, –31
A
B
_ 3. The Cartesian cquation of the plane with normal vector - [1, 2, 1] and passing through the point (3, 2, 1) is:
x+ 2y +z+ 8 = 0
x+ 2y + z- 8 - 0
3x + 2y +z-8 =0
3x + 2y +z+8 = 0
A
B
D
_ 4. The equation of a plane is [x, y, z] = [3, 1, 3] + s[=1, 1, 2] + [2, 1, 1]. Find a normal vector to the plane.
[3, 1, 3]
[-1, 5, -3]
[-1, 1, 2]
[2, 1, 1]
A
В
D
5. The equation of a plane is x+ 2y+ 3z- 6 = 0. Find the y-intereept of the plane.
-1
C
3
В
2
D
-3
_ 6. Two planes are parallel if their normals
are perpendicular
are collincar
dot product is zero
are different
в
D
7. Which of the following determines a plane?
A a line and a point not on the line
B two intersecting lines
C two parallel, non-coincident lines
D all of the above
8. Which of the following is not a plane?
7- (1,3,4) + s(2,-1,2) + (1, 1,1), 5,t e R
7-(2,4,2) + -(1,-2,3) +(3,2,2), 5.t e R
C 7-(3,2.3) +:(4.-4,2) +*(-2,2,-1). ,t e R
A
D7-(-2,1,4) +*(2,2-1) + :(2,2,1). 5.t e R
x+2.
y-1
_ 9. Which of the following points is not on the line
A P(7,7,12)
B P(-2,1,3)
2
C P(-11,-5,-6)
D none of the above
10. On which of the following planes could the point P(0, 4, 3) lie?
A x- 3
в у-3
C z= 3
D none of the above](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F39270a0a-3bd3-4ced-bbae-4e6d934752f5%2Fcd11f325-5c84-4713-b336-ca09e808598d%2Ffcw1gzj_processed.png&w=3840&q=75)
Transcribed Image Text:1. A line passes through the points A(2, 3) and B(-2, 1). Find a vector equation of the line.
[x, y] = [-4, -2] + 12, 3]
[x, yl = [2, 3] + 41-4,-2]
[x, y) = [2, 3] + 1-2, 1]
A
В
D
2. A line has slope 3 and y-intereept 5. Find a vector equation of the line.
[x, y] = [1, -3] + [0, 5)
[x, yl =[-3, 5] + -3, -31
[x, y] = [0, 5] + [1, –3]
[x, yl - [5, 0j + j0, –31
A
B
_ 3. The Cartesian cquation of the plane with normal vector - [1, 2, 1] and passing through the point (3, 2, 1) is:
x+ 2y +z+ 8 = 0
x+ 2y + z- 8 - 0
3x + 2y +z-8 =0
3x + 2y +z+8 = 0
A
B
D
_ 4. The equation of a plane is [x, y, z] = [3, 1, 3] + s[=1, 1, 2] + [2, 1, 1]. Find a normal vector to the plane.
[3, 1, 3]
[-1, 5, -3]
[-1, 1, 2]
[2, 1, 1]
A
В
D
5. The equation of a plane is x+ 2y+ 3z- 6 = 0. Find the y-intereept of the plane.
-1
C
3
В
2
D
-3
_ 6. Two planes are parallel if their normals
are perpendicular
are collincar
dot product is zero
are different
в
D
7. Which of the following determines a plane?
A a line and a point not on the line
B two intersecting lines
C two parallel, non-coincident lines
D all of the above
8. Which of the following is not a plane?
7- (1,3,4) + s(2,-1,2) + (1, 1,1), 5,t e R
7-(2,4,2) + -(1,-2,3) +(3,2,2), 5.t e R
C 7-(3,2.3) +:(4.-4,2) +*(-2,2,-1). ,t e R
A
D7-(-2,1,4) +*(2,2-1) + :(2,2,1). 5.t e R
x+2.
y-1
_ 9. Which of the following points is not on the line
A P(7,7,12)
B P(-2,1,3)
2
C P(-11,-5,-6)
D none of the above
10. On which of the following planes could the point P(0, 4, 3) lie?
A x- 3
в у-3
C z= 3
D none of the above
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