of the line passing through the point A(7, 1, -2) and perpendicular to the plane with equation 2x - 3y + z-1=0. 5. Determine the Cartesian equation of each of the following planes: a. through the point P(0, 1, -2), with normal = (-1, 3, 3) b. through the points (3, 0, 1) and (0, 1, -1), and perpendicular to the plane with equation x-y-z + 1 = 0 c. through the points (1, 2, 1) and (2, 1, 4), and parallel to the x-axis 6. Determine the Cartesian equation of the plane that passes through the origin and contains the line 7=(3, 7, 1) + (2, 2, 3), 1ER. 7. Find the vector and parametric equations of the plane that is now yz-plane and contain th
of the line passing through the point A(7, 1, -2) and perpendicular to the plane with equation 2x - 3y + z-1=0. 5. Determine the Cartesian equation of each of the following planes: a. through the point P(0, 1, -2), with normal = (-1, 3, 3) b. through the points (3, 0, 1) and (0, 1, -1), and perpendicular to the plane with equation x-y-z + 1 = 0 c. through the points (1, 2, 1) and (2, 1, 4), and parallel to the x-axis 6. Determine the Cartesian equation of the plane that passes through the origin and contains the line 7=(3, 7, 1) + (2, 2, 3), 1ER. 7. Find the vector and parametric equations of the plane that is now yz-plane and contain th
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
#5
Transcribed Image Text:Review Exercise
1. Determine vector and parametric equations of the plane that contains the
points A(1, 2, -1), B(2, 1, 1), and C(3, 1, 4).
2. In question 1, there are a variety of different answers possible, depending on
the points and direction vectors chosen. Determine two Cartesian equations
for this plane using two different vector equations, and verify that these two
equations are identical.
3. a. Determine the vector, parametric, and symmetric equations of the line
passing through points A(-3, 2, 8) and B(4, 3, 9).
b. Determine the vector and parametric equations of the plane containing the
points A(-3, 2, 8), B(4, 3, 9), and C(-2,-1, 3).
c. Explain why a symmetric equation cannot exist for a plane.
4. Determine the vector, parametric, and symmetric equations of the line passing
through the point A(7, 1, -2) and perpendicular to the plane with equation
2x - 3y + z-1 = 0.
5. Determine the Cartesian equation of each of the following planes:
a. through the point P(0, 1, -2), with normal = (-1, 3, 3)
b. through the points (3, 0, 1) and (0, 1, -1), and perpendicular to the plane
with equation x-y-z+1=0
c. through the points (1, 2, 1) and (2, 1, 4), and parallel to the x-axis
6. Determine the Cartesian equation of the plane that passes through the origin and
contains the line = (3, 7, 1) + (2, 2, 3), tER.
7. Find the vector and parametric equations of the plane that is parallel to the
yz-plane and contains the point A(-1, 2, 1).
8. Determine the Cartesian equation of the plane that contains the line
7=(2, 3, 2) + t(1, 1, 4), tER, and the point (4, -3, 2).
9. Determine the Cartesian equation of the plane that contains the following lines:
L₁:7=(4, 4, 5) + 1(5, -4, 6), te R, and
L₂:7 (4,4,5) + s(2, -3, -4), SER
10. Determine an equation for the line that is perpendicular to the plane
3x - 2y + z = 1 passing through (2, 3, -3). Give your answer in vector,
parametric, and symmetric form.
11. A plane has 3x + 2yz + 6 = 0 as its Cartesian equation. Determine
the vector and parametric equations of this plane.
NEL
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