Find a vector function that represents the curve of intersection of the two surfaces.The cone y = V= v2x2 +9z2 and the plane y = 5+3zr(t) = (1t22' 156.1r(t) = (t,1t22' 156.15r(t) = (!+ 구t,15%3D6.r(t) = (t, - +2' 156.r(t)%3D= (t,ť +156.

Given data: Equation of cone is y=2x2+9z2. Equation of plane is y=5+3z.

Find a vector function that represents the curve of intersection of the two surfaces. The cone y = v 2x2+922 and the plane y = 5+3z 5 r(t) : 2' 15 1 r(t) = (t, 1,2 2' 15 %3D - r(1) = (* + 1 t, 15 2 r(t) = (t, - 15 + I| 1 5 t, 2 15 r(t) = %3D 6.

Find a vector function that represents the curve of intersection of the two surfaces. The cone y = v 2x2+922 and the plane y = 5+3z 5 r(t) : 2' 15 1 r(t) = (t, 1,2 2' 15 %3D - r(1) = (* + 1 t, 15 2 r(t) = (t, - 15 + I| 1 5 t, 2 15 r(t) = %3D 6.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter9: Systems Of Equations And Inequalities

Section: Chapter Questions

Problem 39RE

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Vector Calculus

Vector calculus is an important branch of mathematics and it relates two important branches of mathematics namely vector and calculus.

Question

Find a vector function that represents the curve of intersection of the two surfaces.
The cone y = V
= v
2x2 +9z2 and the plane y = 5+3z
r(t) = (
1
t2
2' 15
6.
1
r(t) = (t,
1
t2
2' 15
6.
1
5
r(t) = (!
+ 구
t,
15
%3D
6.
r(t) = (t, - +
2' 15
6.
r(t)%3D
= (
t,
ť +
15
6.

Expert Solution

Step 1

Given data:

Equation of cone is $y = \sqrt{2 x^{2} + 9 z^{2}}$ .

Equation of plane is $y = 5 + 3 z$ .

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