Knowledge/Understanding Multiple Choice: 1. A line passes through the points A (7, -4) & B (-5, -2). Find a vector equation of the line. a) [x.y] = [7,-4] + t[-5, -2] c) [x. y] [-5,-2] + t[-12,2] b) [x.y] = [7, 4] + t[-2, -6] d) [x.y] = [12, −2] + t[7,4] 2. A line has slope -3 and x-intercept 5. Find a vector equation of the line. a) [x.y] = [-3,1] + t[5,0] b) [x.y] = [0,5] + t[−3,1] c) [x.y] = [5,0] + t[−1,3] d) [x.y] = [−1, −3] + t[0,5] 3. Write the scalar equation of the plane with normal vector ñ = [3, 2, 1] and passing through the point (4, 5, 6). a) 3x+2yz - 28 = 0 c) 3x+2y+z+28 = 0 b) 4x+5y+6z + 28 = 0 d) 4x+5y + 6z - 28 = 0 4. A plane passes through the origin and has the direction vectors [-1, -2, -3] and [-1, 3, -2]. Find a scalar equation of the plane. a) x 2y3z = 0 b) 13x + y5z = 0 c) x+3y2z = 0 d) 5y + z = 0 (x = s+t 5. The parametric equations of a plane л: y = 1+t. Find a scalar equation of the plane. z = 1-s a) xyz-2=0 b) x + y + z = 0 d) x y z +2=0 c) x y + z = 0 6. Find the intersection point of the two lines: 11: =4-2t (x=5-t x=1+s and 12: (y = −1 + s a) (5,4) b) (1,-1) c) (4,2) d) (1,1) 7. In three-space, find the intersection point of the two lines: [x, y, z] = [3, 4, 0] + t [1, 1, 2] and [x, y, z]=[-1, 4, -20] + s [0, -1, 3]: a) (-1,0,-8) c) (-4,-5,-8) b) (2,0,-3) d) (-4, -5,1) (x = 1+2t 8. In three-space, find the intersection point of the two lines: y = -3+t & z = -3 a) (1,3,-3) b) (2,1,-3) c) (2,-1,0) d) (-7,-7,-3) 9. By analyzing the normals, determine if the two planes: T₁x+2y+3z- 3 = 0 & П2: 2x y+z-7=0 a) intersect in a line b) are parallel and distinct c) are coincident d) intersect at a point (x = 2+3s y = −1 + 2s Z = S 10. By analyzing the normals, determine if the three planes: П₁ x + 2y + 3z-4=0 & π₂: 2x + 4y + 6z + 8 = 0 & π3: 4x+8y + 12z - 10 = 0 a) intersect in a line c) are coincident b) are parallel and distinct d) intersect at a point
Knowledge/Understanding Multiple Choice: 1. A line passes through the points A (7, -4) & B (-5, -2). Find a vector equation of the line. a) [x.y] = [7,-4] + t[-5, -2] c) [x. y] [-5,-2] + t[-12,2] b) [x.y] = [7, 4] + t[-2, -6] d) [x.y] = [12, −2] + t[7,4] 2. A line has slope -3 and x-intercept 5. Find a vector equation of the line. a) [x.y] = [-3,1] + t[5,0] b) [x.y] = [0,5] + t[−3,1] c) [x.y] = [5,0] + t[−1,3] d) [x.y] = [−1, −3] + t[0,5] 3. Write the scalar equation of the plane with normal vector ñ = [3, 2, 1] and passing through the point (4, 5, 6). a) 3x+2yz - 28 = 0 c) 3x+2y+z+28 = 0 b) 4x+5y+6z + 28 = 0 d) 4x+5y + 6z - 28 = 0 4. A plane passes through the origin and has the direction vectors [-1, -2, -3] and [-1, 3, -2]. Find a scalar equation of the plane. a) x 2y3z = 0 b) 13x + y5z = 0 c) x+3y2z = 0 d) 5y + z = 0 (x = s+t 5. The parametric equations of a plane л: y = 1+t. Find a scalar equation of the plane. z = 1-s a) xyz-2=0 b) x + y + z = 0 d) x y z +2=0 c) x y + z = 0 6. Find the intersection point of the two lines: 11: =4-2t (x=5-t x=1+s and 12: (y = −1 + s a) (5,4) b) (1,-1) c) (4,2) d) (1,1) 7. In three-space, find the intersection point of the two lines: [x, y, z] = [3, 4, 0] + t [1, 1, 2] and [x, y, z]=[-1, 4, -20] + s [0, -1, 3]: a) (-1,0,-8) c) (-4,-5,-8) b) (2,0,-3) d) (-4, -5,1) (x = 1+2t 8. In three-space, find the intersection point of the two lines: y = -3+t & z = -3 a) (1,3,-3) b) (2,1,-3) c) (2,-1,0) d) (-7,-7,-3) 9. By analyzing the normals, determine if the two planes: T₁x+2y+3z- 3 = 0 & П2: 2x y+z-7=0 a) intersect in a line b) are parallel and distinct c) are coincident d) intersect at a point (x = 2+3s y = −1 + 2s Z = S 10. By analyzing the normals, determine if the three planes: П₁ x + 2y + 3z-4=0 & π₂: 2x + 4y + 6z + 8 = 0 & π3: 4x+8y + 12z - 10 = 0 a) intersect in a line c) are coincident b) are parallel and distinct d) intersect at a point
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.3: Lines
Problem 22E
Related questions
Question
![Knowledge/Understanding
Multiple Choice:
1. A line passes through the points A (7, -4) & B (-5, -2). Find a vector equation of the line.
a) [x.y] = [7,-4] + t[-5, -2]
c) [x. y] [-5,-2] + t[-12,2]
b) [x.y] = [7, 4] + t[-2, -6]
d) [x.y] = [12, −2] + t[7,4]
2. A line has slope -3 and x-intercept 5. Find a vector equation of the line.
a) [x.y] = [-3,1] + t[5,0]
b) [x.y] = [0,5] + t[−3,1]
c) [x.y] = [5,0] + t[−1,3]
d) [x.y] = [−1, −3] + t[0,5]
3. Write the scalar equation of the plane with normal vector ñ = [3, 2, 1] and passing
through the point (4, 5, 6).
a) 3x+2yz - 28 = 0
c) 3x+2y+z+28 = 0
b) 4x+5y+6z + 28 = 0
d) 4x+5y + 6z - 28 = 0
4. A plane passes through the origin and has the direction vectors [-1, -2, -3] and [-1, 3, -2].
Find a scalar equation of the plane.
a) x
2y3z = 0
b) 13x + y5z = 0
c) x+3y2z = 0
d) 5y + z = 0](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fdf41df8f-e300-4854-aaa2-c9c3c769a22c%2F5cbecd25-b69a-46c8-9849-5f5228d0b967%2Fi7s85bo_processed.png&w=3840&q=75)
Transcribed Image Text:Knowledge/Understanding
Multiple Choice:
1. A line passes through the points A (7, -4) & B (-5, -2). Find a vector equation of the line.
a) [x.y] = [7,-4] + t[-5, -2]
c) [x. y] [-5,-2] + t[-12,2]
b) [x.y] = [7, 4] + t[-2, -6]
d) [x.y] = [12, −2] + t[7,4]
2. A line has slope -3 and x-intercept 5. Find a vector equation of the line.
a) [x.y] = [-3,1] + t[5,0]
b) [x.y] = [0,5] + t[−3,1]
c) [x.y] = [5,0] + t[−1,3]
d) [x.y] = [−1, −3] + t[0,5]
3. Write the scalar equation of the plane with normal vector ñ = [3, 2, 1] and passing
through the point (4, 5, 6).
a) 3x+2yz - 28 = 0
c) 3x+2y+z+28 = 0
b) 4x+5y+6z + 28 = 0
d) 4x+5y + 6z - 28 = 0
4. A plane passes through the origin and has the direction vectors [-1, -2, -3] and [-1, 3, -2].
Find a scalar equation of the plane.
a) x
2y3z = 0
b) 13x + y5z = 0
c) x+3y2z = 0
d) 5y + z = 0
![(x = s+t
5. The parametric equations of a plane л: y = 1+t. Find a scalar equation of the plane.
z = 1-s
a) xyz-2=0
b) x + y + z = 0
d) x y z +2=0
c) x y + z = 0
6. Find the intersection point of the two lines: 11: =4-2t
(x=5-t
x=1+s
and 12:
(y = −1 + s
a) (5,4)
b) (1,-1)
c) (4,2)
d) (1,1)
7. In three-space, find the intersection point of the two lines: [x, y, z] = [3, 4, 0] + t [1, 1, 2]
and [x, y, z]=[-1, 4, -20] + s [0, -1, 3]:
a) (-1,0,-8)
c) (-4,-5,-8)
b) (2,0,-3)
d) (-4, -5,1)
(x = 1+2t
8. In three-space, find the intersection point of the two lines: y = -3+t &
z = -3
a) (1,3,-3)
b) (2,1,-3)
c) (2,-1,0)
d) (-7,-7,-3)
9. By analyzing the normals, determine if the two planes:
T₁x+2y+3z- 3 = 0
&
П2: 2x y+z-7=0
a) intersect in a line
b) are parallel and distinct
c) are coincident
d) intersect at a point
(x = 2+3s
y = −1 + 2s
Z = S
10. By analyzing the normals, determine if the three planes:
П₁ x + 2y + 3z-4=0 & π₂: 2x + 4y + 6z + 8 = 0 & π3: 4x+8y + 12z - 10 = 0
a) intersect in a line
c) are coincident
b) are parallel and distinct
d) intersect at a point](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fdf41df8f-e300-4854-aaa2-c9c3c769a22c%2F5cbecd25-b69a-46c8-9849-5f5228d0b967%2Fl5jjdj_processed.png&w=3840&q=75)
Transcribed Image Text:(x = s+t
5. The parametric equations of a plane л: y = 1+t. Find a scalar equation of the plane.
z = 1-s
a) xyz-2=0
b) x + y + z = 0
d) x y z +2=0
c) x y + z = 0
6. Find the intersection point of the two lines: 11: =4-2t
(x=5-t
x=1+s
and 12:
(y = −1 + s
a) (5,4)
b) (1,-1)
c) (4,2)
d) (1,1)
7. In three-space, find the intersection point of the two lines: [x, y, z] = [3, 4, 0] + t [1, 1, 2]
and [x, y, z]=[-1, 4, -20] + s [0, -1, 3]:
a) (-1,0,-8)
c) (-4,-5,-8)
b) (2,0,-3)
d) (-4, -5,1)
(x = 1+2t
8. In three-space, find the intersection point of the two lines: y = -3+t &
z = -3
a) (1,3,-3)
b) (2,1,-3)
c) (2,-1,0)
d) (-7,-7,-3)
9. By analyzing the normals, determine if the two planes:
T₁x+2y+3z- 3 = 0
&
П2: 2x y+z-7=0
a) intersect in a line
b) are parallel and distinct
c) are coincident
d) intersect at a point
(x = 2+3s
y = −1 + 2s
Z = S
10. By analyzing the normals, determine if the three planes:
П₁ x + 2y + 3z-4=0 & π₂: 2x + 4y + 6z + 8 = 0 & π3: 4x+8y + 12z - 10 = 0
a) intersect in a line
c) are coincident
b) are parallel and distinct
d) intersect at a point
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