1. A line passes through the points A(2, 3) and B(-2, 1). Determine a vector equation of the line. a. [x, y] [2, 3] + {[-2, 1] b. [x, y] =[-2, 1] + [2, 3] c. [x, y] d. [x, y] [4, -2] + [2, 3] [2, 3] + [-4, -2]
1. A line passes through the points A(2, 3) and B(-2, 1). Determine a vector equation of the line. a. [x, y] [2, 3] + {[-2, 1] b. [x, y] =[-2, 1] + [2, 3] c. [x, y] d. [x, y] [4, -2] + [2, 3] [2, 3] + [-4, -2]
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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![1. A line passes through the points A(2, 3) and B(-2, 1). Determine a vector equation of
the line.
a.
[x, y]
b. [x, y]
[2, 3] + [-2, 1]
[-2, 1] + [2, 3]
C.
d.
2. A line has y-intercept 11 and z-intercept -13. Determine a vector equation of the line.
[x, y, z] [0, 11, 0] + f[0, 11, 13]
[x, y, z) = [0, 0, -13] + 10, 11,0]
d. [x, y, z]= [0, 11, 0] + f[0, 0, -13]
a.
C.
b.
[x, y, z) = [0, 11, 13] + [0, 11, 0]
C.
d.
3. Write the scalar equation of the line with normal vector = [1.3] and passing through
the point (2, -1).
a. 2x-y+1=0
b.
x+3y-1=0
4. A plane passes through the three points A(1, 1, 1), B(2, 3, 4), and C(1, 0, 1). Determine
a vector equation of the plane.
a. [x, y, z] [1, 1, 1] + s[1, 2, 3] + f[0,-1,0]
b.
[x, y, z) = [1, 1, 1] + s[2, 3, 4] + f[1,0, 1]
[x, y, z]= [1, 2, 3] + s[2, 3, 4] + f[1,0, 1]
[x, y, z] [1, 1, 1] + s[1, 0, 1] + [1, 2, 3]
=
-1
[x, y]
[x, y]
a.
b. 2
[4, -2] + [2, 3]
[2, 3] + [-4, -2]
5. A plane passes through the origin and has the direction vectors [1, 2, 3] and [-1, 3, -2].
Determine a scalar equation of the plane.
a.
x + 2y+3z = 0
b. -x1 3y-22-3
C. x + 3y + 1 = 0
d. 2x-x-1=0
C.
d.
a. [3,1,3]
b. [-1,5,-3]
6. The vector equation of a plane is [x. y. z] = [1, 1, 1]+s[2, 1, 3] + :[-3, 2, 4]. Determine a scalar
equation of the plane.
a. 2x + y + 32 + 3 = 0
b.
2x + 17y - 72 = 0
C.
d.
13x+y - 5z = 7
13x y-52-3
7. The equation of a plane is x+2y+32-6= 0. Determine the y-intercept of the plane.
C. 3
d. -3
2x + 17y7z + 12 = 0
2x + 17y72-12 = 0
8. The equation of a plane is [x, y, z] = [3, 1, 3] + s[−1. ., Z + [2, 1, 1]. Determine a normal
vector to the plane.
C. [-1,1,2]
d. [2,1,1]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F13712dc3-bee6-43fd-bec1-910ac6a24a64%2Fa6d6df5e-fd6a-4985-88f6-3107a19fd2b0%2Fcsvxnia_processed.png&w=3840&q=75)
Transcribed Image Text:1. A line passes through the points A(2, 3) and B(-2, 1). Determine a vector equation of
the line.
a.
[x, y]
b. [x, y]
[2, 3] + [-2, 1]
[-2, 1] + [2, 3]
C.
d.
2. A line has y-intercept 11 and z-intercept -13. Determine a vector equation of the line.
[x, y, z] [0, 11, 0] + f[0, 11, 13]
[x, y, z) = [0, 0, -13] + 10, 11,0]
d. [x, y, z]= [0, 11, 0] + f[0, 0, -13]
a.
C.
b.
[x, y, z) = [0, 11, 13] + [0, 11, 0]
C.
d.
3. Write the scalar equation of the line with normal vector = [1.3] and passing through
the point (2, -1).
a. 2x-y+1=0
b.
x+3y-1=0
4. A plane passes through the three points A(1, 1, 1), B(2, 3, 4), and C(1, 0, 1). Determine
a vector equation of the plane.
a. [x, y, z] [1, 1, 1] + s[1, 2, 3] + f[0,-1,0]
b.
[x, y, z) = [1, 1, 1] + s[2, 3, 4] + f[1,0, 1]
[x, y, z]= [1, 2, 3] + s[2, 3, 4] + f[1,0, 1]
[x, y, z] [1, 1, 1] + s[1, 0, 1] + [1, 2, 3]
=
-1
[x, y]
[x, y]
a.
b. 2
[4, -2] + [2, 3]
[2, 3] + [-4, -2]
5. A plane passes through the origin and has the direction vectors [1, 2, 3] and [-1, 3, -2].
Determine a scalar equation of the plane.
a.
x + 2y+3z = 0
b. -x1 3y-22-3
C. x + 3y + 1 = 0
d. 2x-x-1=0
C.
d.
a. [3,1,3]
b. [-1,5,-3]
6. The vector equation of a plane is [x. y. z] = [1, 1, 1]+s[2, 1, 3] + :[-3, 2, 4]. Determine a scalar
equation of the plane.
a. 2x + y + 32 + 3 = 0
b.
2x + 17y - 72 = 0
C.
d.
13x+y - 5z = 7
13x y-52-3
7. The equation of a plane is x+2y+32-6= 0. Determine the y-intercept of the plane.
C. 3
d. -3
2x + 17y7z + 12 = 0
2x + 17y72-12 = 0
8. The equation of a plane is [x, y, z] = [3, 1, 3] + s[−1. ., Z + [2, 1, 1]. Determine a normal
vector to the plane.
C. [-1,1,2]
d. [2,1,1]
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