Find both parametric and rectangular representations for the plane tangent to r(u,v)=u2i+ucos(v)j+usin(v)kr(u,v)=u2i+ucos⁡(v)j+usin⁡(v)k at the point P(4,−2,0)P(4,−2,0).One possible parametric representation has the form⟨4−4u⟨4−4u , , 4v⟩4v⟩(Note that parametric representations are not unique. If your first and third components look different than the ones presented here, you will need to adjust your parameters so that they do match, and then the other components should match the ones expected here as well.)The equation for this plane in rectangular coordinates has the form x+x+ y+y+ z+z+ =0 Find both parametric and rectangular representations for the plane tangent to r(u, v) = u²i + u cos(v)j + u sin(v)k at the point P(4, -2, 0).One possible parametric representation has the form(4 – 4u4v)(Note that parametric representations are not unique. If your first and third components look different than the ones presented here, you will need to adjust your parameters so that they do match, and then theother components should match the ones expected here as well.)The equation for this plane in rectangular coordinates has the formy+(Be sure your coefficients have been set so that (1) the coefficient of x is positive, (2) all coefficients are integers, and (3) there are no more common factors that can still be divided out.)

Answered: Find both parametric and rectangular…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter11: Topics From Analytic Geometry

Section11.5: Polar Coordinates

Problem 97E

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Find both parametric and rectangular representations for the plane tangent to r(u,v)=u2i+ucos(v)j+usin(v)kr(u,v)=u2i+ucos⁡(v)j+usin⁡(v)k at the point P(4,−2,0)P(4,−2,0).

One possible parametric representation has the form

⟨4−4u⟨4−4u , , 4v⟩4v⟩

(Note that parametric representations are not unique. If your first and third components look different than the ones presented here, you will need to adjust your parameters so that they do match, and then the other components should match the ones expected here as well.)

The equation for this plane in rectangular coordinates has the form

x+x+ y+y+ z+z+ =0

Find both parametric and rectangular representations for the plane tangent to r(u, v) = u²i + u cos(v)j + u sin(v)k at the point P(4, -2, 0).
One possible parametric representation has the form
(4 – 4u
4v)
(Note that parametric representations are not unique. If your first and third components look different than the ones presented here, you will need to adjust your parameters so that they do match, and then the
other components should match the ones expected here as well.)
The equation for this plane in rectangular coordinates has the form
y+
(Be sure your coefficients have been set so that (1) the coefficient of x is positive, (2) all coefficients are integers, and (3) there are no more common factors that can still be divided out.)

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