#201 Show that the subsets of the plane € ( = {cx₁y) / 2 = x ² + y ² <= 4 } are open:

Q: State the equstion of the yz plane

A: We have to find equation of yz plane

Q: Show that the line [x, y, z]= [5,-1,3]+[4,-5,2] lies on the planes 3x+2y-z = 10 and 7x+4y-4z=19.

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Q: 2) Calculate the distonce d of the pint ? (-l,(, -2) from the plane passing through the three A(…

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Q: The projection of the point (2, -3, 1) on the yz- plane is Select one: O (0, -3,1) ○ (2,0,1) O (2,…

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Q: Show whether the set {(2, –1, 3), (0, 3, 1), (- 1,1, -2)} in the space R³ is linearly independent.

A: Definition. Let V be a vector space. Vectors v1, v2, . . . ,vk ∈ V are  called linearly dependent if…

Q: 30 0= +시 +씨 2 |and 3x-y-z=3 -8/

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Q: The point on the plane 2x+y+z=1 that is closest to the point (1, 2, 3) is (a, b, c). Then a+b-2c= O…

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Q: Give equations for two distinct planes whose trace in the yz-plane has equation y = 4z

A: Given, two distinct planes have trace in the yz-plane has equation y = 4z

Q: A point moves so that sum of the squares of its distances from the vertices of a triangle is always…

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Q: 4. Find an equation for the plane in R³ spanned by the points (1,5, 1) and (1, 4, 2).

A: The two vectors are given as v1 = 151v2 = 142 Let xyz∈span{v1 , v2} Then xyz = mv1+nv2= m151+n142=…

Q: Among all the points on the graph of z= 12-x² - y² that lie above the plane x + 4y +62 = 0, find the…

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Q: Suppose the solution set of x1 + x2+2x4 What are the equations of the plane at (1,2,3,4) which is…

A: First we find direction vectors of the plane of solutions.

Q: 2) Find the point of intersection of the plane x - 5y + 3z = -127 and the line r(t) = (-2,-8, 7)t +…

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Q: point P(1, 1, –3) and orthogonal to the plane 3y – 4x + 2z = 3. |

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Q: Fud the Line pussing through the posnt (!,-l,o) and purrllel to the Eme of intersection of planes (X…

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Q: 9 find the cqu. f Plane that Contains the two line Ś: X-1=3+ 6=そ X=リニで-4 and Passes through origin?…

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