2) Work ANY THREE of the following: a. Find an equation for the plane through the following points: (1, 2, 4), (2, -2, -2), (-2, 5, 2) Determine whether the given lines intersect, are parallel, or are skew. If they intersect, b. determine where. L₁ = (7-2t, 9+ 6 t, 1-2 t) and L2 = (1+6t, 3-3 t, 5-t) e. C. Find the distance between the following planes: 4x-6y +z = 1 and -8 x+4y-6z = 8. (Hint: it suffices to find the distance from one point in the first plane to the second plane...) d. Find a vector equation for the line of intersection of the following planes: 2x+4y-z = 1 and x-y-2z=4 Find the vector projection of the vector (1, 2, 3) that lies in the plane 2 x-6y +z = 0. (Hint: it's easy to find the projection of the vector onto the normal to the plane. Now what do you do?)
2) Work ANY THREE of the following: a. Find an equation for the plane through the following points: (1, 2, 4), (2, -2, -2), (-2, 5, 2) Determine whether the given lines intersect, are parallel, or are skew. If they intersect, b. determine where. L₁ = (7-2t, 9+ 6 t, 1-2 t) and L2 = (1+6t, 3-3 t, 5-t) e. C. Find the distance between the following planes: 4x-6y +z = 1 and -8 x+4y-6z = 8. (Hint: it suffices to find the distance from one point in the first plane to the second plane...) d. Find a vector equation for the line of intersection of the following planes: 2x+4y-z = 1 and x-y-2z=4 Find the vector projection of the vector (1, 2, 3) that lies in the plane 2 x-6y +z = 0. (Hint: it's easy to find the projection of the vector onto the normal to the plane. Now what do you do?)
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:2) Work ANY THREE of the following:
a. Find an equation for the plane through the following points: (1, 2, 4), (2, -2, -2), (-2, 5, 2)
Determine whether the given lines intersect, are parallel, or are skew. If they intersect,
b. determine where.
L₁ = (7-2t, 9+ 6 t, 1-2 t) and L2 = (1+6t, 3-3 t, 5-t)
e.
C.
Find the distance between the following planes: 4x-6y +z = 1 and -8 x+4y-6z = 8. (Hint:
it suffices to find the distance from one point in the first plane to the second plane...)
d. Find a vector equation for the line of intersection of the following planes: 2x+4y-z = 1 and
x-y-2z=4
Find the vector projection of the vector (1, 2, 3) that lies in the plane 2 x-6y +z = 0. (Hint: it's
easy to find the projection of the vector onto the normal to the plane. Now what do you do?)
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