1. Find an equation of the line with the given properties, in the indicated form. a. A(2,4,-3), B(3,-1,1) in parametric form. b. A(-8,2,4), B(3,-2,5) in symmetric form. 1 c. Parallel to x + 2 = y = z − 3 through the point (1,-1,1) in both forms. 2. Find the equation of the plane. a. Passes through the point (5, -3, -4) and perpendicular to vector (2, -1,3) b. Passes through the point (-6,0,8) and perpendicular to line x = 5 - 2t, y = −4+2t, z = 0. c. Passes through (2,3,-2), (3,4,2) and (-1,-1,0) d. Contains the y-axis and makes an angle of π/6 with the positive x-axis. e. Contains the lines given by x-1 -2 x-2y-1 z-2 y-4=z and = -3 4 -1 f. Passes through (2,2,1) and (−1,1, −1) and is perpendicular to the plane 2x-3y+ z = 3. 3. Find a set of parametric equations for the line of intersection of the planes 3x+2y-z 7,x-4y+2z=0. At what angle do they intersect? 4. Find the distance between the point and the plane/line using the formulas D = ||PQ-n|| respectively where Q is any point in the plane/line. a. P(2,8,4) 2x+y+z=5 = PQXV ||7|| and D = b. P(-2,1,3) x=1-t,y=2+t,z=-2t 5. Find the domain of the vector-valued function. Find 7(1)||. r(t)=√4-f²i+t² j−6tk b. r(t)=√ti+j+(t+2)k t+1 c. r(t)=(Int-1)i+tj d. r(t)=(1−t)i+√tk
1. Find an equation of the line with the given properties, in the indicated form. a. A(2,4,-3), B(3,-1,1) in parametric form. b. A(-8,2,4), B(3,-2,5) in symmetric form. 1 c. Parallel to x + 2 = y = z − 3 through the point (1,-1,1) in both forms. 2. Find the equation of the plane. a. Passes through the point (5, -3, -4) and perpendicular to vector (2, -1,3) b. Passes through the point (-6,0,8) and perpendicular to line x = 5 - 2t, y = −4+2t, z = 0. c. Passes through (2,3,-2), (3,4,2) and (-1,-1,0) d. Contains the y-axis and makes an angle of π/6 with the positive x-axis. e. Contains the lines given by x-1 -2 x-2y-1 z-2 y-4=z and = -3 4 -1 f. Passes through (2,2,1) and (−1,1, −1) and is perpendicular to the plane 2x-3y+ z = 3. 3. Find a set of parametric equations for the line of intersection of the planes 3x+2y-z 7,x-4y+2z=0. At what angle do they intersect? 4. Find the distance between the point and the plane/line using the formulas D = ||PQ-n|| respectively where Q is any point in the plane/line. a. P(2,8,4) 2x+y+z=5 = PQXV ||7|| and D = b. P(-2,1,3) x=1-t,y=2+t,z=-2t 5. Find the domain of the vector-valued function. Find 7(1)||. r(t)=√4-f²i+t² j−6tk b. r(t)=√ti+j+(t+2)k t+1 c. r(t)=(Int-1)i+tj d. r(t)=(1−t)i+√tk
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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I need help with this problem and an explanation for the solution described below. (Calculus 3)
Transcribed Image Text:1. Find an equation of the line with the given properties, in the indicated form.
a. A(2,4,-3), B(3,-1,1) in parametric form.
b. A(-8,2,4), B(3,-2,5) in symmetric form.
1
c. Parallel to x + 2 = y = z − 3 through the point (1,-1,1) in both forms.
2. Find the equation of the plane.
a. Passes through the point (5, -3, -4) and perpendicular to vector (2, -1,3)
b. Passes through the point (-6,0,8) and perpendicular to line x = 5 - 2t, y = −4+2t, z = 0.
c. Passes through (2,3,-2), (3,4,2) and (-1,-1,0)
d. Contains the y-axis and makes an angle of π/6 with the positive x-axis.
e. Contains the lines given by
x-1
-2
x-2y-1 z-2
y-4=z and
=
-3
4
-1
f. Passes through (2,2,1) and (−1,1, −1) and is perpendicular to the plane 2x-3y+ z = 3.
3. Find a set of parametric equations for the line of intersection of the planes
3x+2y-z 7,x-4y+2z=0. At what angle do they intersect?
4. Find the distance between the point and the plane/line using the formulas D =
||PQ-n||
respectively where Q is any point in the plane/line.
a. P(2,8,4) 2x+y+z=5
=
PQXV
||7||
and D =
b. P(-2,1,3) x=1-t,y=2+t,z=-2t
5. Find the domain of the vector-valued function. Find 7(1)||.
r(t)=√4-f²i+t² j−6tk
b. r(t)=√ti+j+(t+2)k
t+1
c. r(t)=(Int-1)i+tj
d. r(t)=(1−t)i+√tk
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