Question: Consider the ellipsoid 2x + y + 3z = 21. Find all the points where the tangent plane to this ellipsoid is parallel to

Consider the ellipsoid 2x + y + 3z = 21. Find all the points where the tangent plane to this ellipsoid is parallel to the plane 4x+6z = 0. Hint: (-2*sqrt(28)/3,sqrt(28)/6,2*sqrt(28)), (2*sqrt(28)/3,-sqrt(: (If there are several points, separate them by commas.) Hint: The normal vectors of the tangent plane and the given plane must be parallel, and the point must actually lie on the ellipsoid. This should give you four equations in four unknowns that you can solve.

Step by Step Solution

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

Soin Given the equation of ellipsoid 28177 32 21 Jet fl 2... View full answer

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Students Have Also Explored These Related Mathematics Questions!

content area top Part 1 A bankruptcy process is complex, timeminusconsuming, and costly. The costs of bankruptcy include ________. Question content area bottom Part 1 A. costs of hiring legal...

This question concerns lexical grammars. (a) Tree Adjoining Grammars contain two types of elementary tree. (i) What are these trees called? [1 mark] (ii) If one were building a grammar for English...

Describe, in detail, how the heapsort algorithm works. [10 marks] Show that the worst-case cost of heapsort is O(n log n). [6 marks] Would it be possible to implement a variant of heapsort based on a...

Software programs are becoming extremely complex to design, develop, and build. Many organizations either dont have the in-house staff to accomplish the task (i.e., build) or they decide to focus on...

MA 261 PRACTICE PROBLEMS 1. If the line ` has symmetric equations y x1 z+2 2 = 3 = 7 , nd a vector equation for the line `0 that contains the point (2; 1; 3) and is parallel to `. A. ~ = (1 + 2t)~...

Harold Washington College Math 209 Practice Problems Test 1 Part 2 Name: Date: Solve the following problems. (1) Let ~ u, ~ v be vectors. Prove the identity ||~ u~ v||2 +|~ u~ v|2 = ||~ u||2||~ v||2....

Please if you can help do most of these questions I am stuck and don't know how to solve them. 4. Find the points on the ellipsoid 4x2 + 2y2 +3= = 6 where the tangent plane is parallel to the plane...

There are two points on the ellipsoid 2x2 + y2 + 2? - 10 where the tangent plane is parallel to the plane 4x-y+2- 12. Find these two points and enter their coordinates below. Point 1: Make this the...

5. [-/3 Points] DETAILS SCALCET9 14.6.039. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Suppose that over a certain region of space the electrical potential V is given by the following equation. V(x,...

6. [-/1 Points] DETAILS SCALCET9 14.6.045. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER The second directional derivative of f(x, y) is 2( ( x , y ) = Du Duf ( x , y ) . If f(x, y) = x3 + 5x2y + y3 and...

The High Rate of Bacterial Metabolism Bacterial cells have a much higher rate of metabolism than animal cells. Under ideal conditions some bacteria double in size and divide every 20 min, whereas...

For the reaction if percentage dissociations of N,04 are 20%, 45% ,65% ,80% Then the sequence of observed vapour densities (at equilibrium) will be (A) dz0 > d45 > dgs > dso (B) dgo > d65 > d45 > d20...

There frica in equlinges, enployers should spply the: a . principles of just cause. b . standards of employment or nilust. c . policies of equity and responsibility. d . rules of fair employment.

Which of the following is true about gross profit (gross margin)? It is net sales minus operation expenses. It is net sales minus cost of goods sold. It is the same as income from continuing...

Case: Samsung a Strategic Plan for Success 1. A short and concise overview of the company. This should include its origin, its mission statement and the size & reach of the company. 2. Perform a...

Find the value of M(120), M(111), M(97) and M(94). - 10 n> 100 M(n) = (( + 11)) n

Use strong induction to prove that every integer n > 5 can be written as n 4x + 3y for non-negative z, y Z.

Use induction to show that 1- rn+1 an r+1 1-r satisfies the recurrence relation ao = 1 ak = ak-1+rk k> 0. %3D

6 Theory of Machines 5. A shaft carries five masses A, B, C, D and E which revolve at the same radius in planes which are equidistant from one another. The magnitude of the masses in planes A, C and...

Let T be the topological boundary of the tetrahedron in Exercise 13.4.5, with outward-pointing normal, and S be the surface obtained by taking away the slanted face from T (i.e., S has three...

For each of the following, evaluate C F T ds. a) C is the curve formed by intersecting the cylinder x2 + y2 = 1 with z = - x, oriented in the counterclockwise direction when viewed from high on the...

Let p > 0. Show that x/xp is improperly integrable on [1, ) and that cos x/logp x is improperly integrable on [e, ).

Do you believe mass media and social networking will make major alterations to gender roles in the next ten years? Why or why not?

The growing number of multinational corporations presents unique management challenges. Differences in language, work methods, cultural identities, power, and legal systems and standards must be...

Interview someone from a culture different from your own using questions about child-rearing practices. You might inquire about methods of discipline, toys, games, topics discussed at the dinner...