Use t = y to parametrize the part of the line of intersection of the two planes y = 2x – 4 and z = 3x +1 from (2,0, 7) to (3, 2, 10). EXAMPLE 1

Algebra and Trigonometry (6th Edition)
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ChapterP: Prerequisites: Fundamental Concepts Of Algebra
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Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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Use t = y to parametrize the part of the line of intersection of the
two planes y = 2x – 4 and z = 3x +1 from (2, 0, 7) to (3, 2, 10).
EXAMPLE 1
%3D
EXAMPLE 2
The plane x + y
= 1 intersects the paraboloid z =
x² + y?
in a parabola. Parametrize the whole parabola using t = x as
parameter. Could t = y have been used as parameter? What about t = 2?
Parametrize the curve of intersection of the plane x +2y+4z = 4
and the elliptic cylinder x? + 4y² = 4.
EXAMPLE 4
x² + 4y? = 4
x+2y +4z = 4
EXAMPLE 6
Find the length s of that part of the circular helix
r = a costi + a sin tj + bt k
between the points (a, 0, 0) and (a, 0, 2nb).
Transcribed Image Text:Use t = y to parametrize the part of the line of intersection of the two planes y = 2x – 4 and z = 3x +1 from (2, 0, 7) to (3, 2, 10). EXAMPLE 1 %3D EXAMPLE 2 The plane x + y = 1 intersects the paraboloid z = x² + y? in a parabola. Parametrize the whole parabola using t = x as parameter. Could t = y have been used as parameter? What about t = 2? Parametrize the curve of intersection of the plane x +2y+4z = 4 and the elliptic cylinder x? + 4y² = 4. EXAMPLE 4 x² + 4y? = 4 x+2y +4z = 4 EXAMPLE 6 Find the length s of that part of the circular helix r = a costi + a sin tj + bt k between the points (a, 0, 0) and (a, 0, 2nb).
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