Determine the distance from point P(-2, –1, 1) to the plane [x, y, z] = [4, –1, 6] + t[1, 6, 3] + s[-2, 3, 1]

Q: Find the plane tangent to the surface z=x x+ y° at the point (3,4,25). a. 6x+8y-z=25 O b. 6x-8y-z=25…

A: As we know that; The equation of the tangent plane: nxx-x0+nyy-y0+nzz-z0=0 And The normal vector at…

Q: The equation of the plane that contains the point (1, 2, 3) and the line x = 4t, y = t, z = t is…

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Q: Find the equation of the plane in the form z=c+mx+ny containing the line in the xy-plane where x=3,…

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Q: Find a function r(t) that describes the line through P(3,4,5) that is orthogonal to the plane 2x-z=4

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Q: Find a vector parallel to the line of intersection of the planes 2x + 3y – = =11 and 4x + 2y – 3= =…

A: Topic:- vector

Q: Find the mapping that reflects the plane in the line x+y-1=C O (x,y)>(y+1,x+1) (x,y)→(-x+1,-y+1) O…

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Q: F = (x² – y², y² – 2², z² – x²), S is the part of the plane r + y + z = 1 in the first octant.

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Q: Find T, N, and k for the space curves r(t) = (t3/3)i + (t2/2)j, t > 0

A: Given, the space curve r(t) = (t3/3)i + (t2/2)j, t>0 We have to find the T, N, and K for this…

Q: Let L be a line which passes through the point (-4,0, 1) and is perpendicular to the plane x + 2y +…

A: Please refer the attached image for complete solution.

Q: (A) Determine the plane that contain the point A(2,5,1) and the line L, t=x-2, 3t =y-1, t=z+1

A: The equation of the line L given in the parametric form, that is, Thus, the above equation of the…

Q: Let T, denote the plane parallel to the xz-plane through the point (1, 2, 3). Let n2 denote the…

A: To solve this problem first of we find the equation of the plane π1 and π2 in standard form and then…

Q: Evaluate / x2 zdS, where S is the part of the plane z = 4+ 3x + y above the rectangle [0, 4] x [0,…

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Q: find the trace of the plane in the given coordinate plane.  −x + y = 4, xz

A: Find trace of the plane in the coordinate plane -x+y=4 in xz

Q: Let f(x, y, z) = x² + 2y? + 4z2. Find the point on the plane x + y + z = 14 at which f has its…

A: Given: fx,y,z=x2+2y2+4z2and the plane equation x+y+z=14 To find the point x,y,z The Lagrange's…

Q: 3. Find the plane determined by the intersecting lines L: x = -1+t, y = 2+t, z = 1- t; L2: x = 1 -…

A: Since you have posted multiple questions in this question which are not interlinked so I have solved…

Q: For a plane with a normal of n = [1, 2, - 9]   and containing a point P (3, -4, 0), write the…

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Q: Determine the image of the upper half plane {z € C : Im(z) > 0 }

A: In this question, we use the transformation under g(z) we find the image set.

Q: Let T be the plane x – y – z = 7. Which of the following planes are orthogonal to T and pass through…

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Q: Find the distance from y to the plane in R spanned by the set {u1, uz} 4 - 3 -3 y = -9 -4 Uz 2 4 1…

A: Solution   Given,       Find the distance from  γ to the plane  in R3       spanned  by the  set…

Q: 10. Consider the plane P given by r + y – 3z = 0. (a) Find the projection of the vector (2, 1, 0)…

A: Given plane : x+y-3z=0  Projection of A along B is A.B/|B|

Q: H.W: Find the distance from S (1,1,3) to the plane 3x+ 2y+ 6z = 6

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Q: Sketch the plane curve. r(t) = 2ti – tj, [0, 2] y y 2. 1 1 -1 1 4 -1 1 4 5 -1 y -1 2 3 4 1 2 3 4 5…

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Q: Find the point A (a, a, 0) on the line y = x in the xy-plane, such that the vector AB is…

A: Solution is given below:

Q: Find the plane containing the intersecting lines L1: x = -1+t, y= 2+t, z = 1 – t; L2: x = 1 – 4s,…

A: The given intersecting lines are  L1: x=-1+t,y=2+t,z=1-t; -∞<t<∞L2: x=1-4s,y=1+2s,z=2-2s;…

Q: If possible, determine the vector, parametric,symmetrical and reduced line r that: a) passes…

A: Given the lines S1:t·1,2,3, t∈ℝ and S2:y=x+2, z=x. To find a line L passing through the point P1,1,1…

Q: Let R = (c, 1,-1) where c denotes a real number. Let ä denote the plane x + y – z = 2. Find the…

A: Given Information -  The distance from the point R = (c,1,-1) to the plane x+y-z = 2 is 2. We have…

Q: Find an equation of the plane through (– 1, 3, –4) that is perpendicular to the planes 8x – y + z =…

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Q: a) Evaluate f, (2x – z) dS, where S is part of the plane 3x + 2y + z = 1 that lies above the…

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Q: Evaluate x* zdS, where S is the part of the plane z = 1+4x + 3y above the rectangle [0, 3] x [0, 5]

A: Please see the below picture for detailed solution.

Q: Find all planes in R3 whose intersection with the xy-plane is the liner( t) = t ( 2, 1, 0) .

A: GIVEN  Intersection with the xy-plane is the line r( t) = t ( 2, 1, 0)

Q: Show there is no plane perpendicular to n=i+jn=i+j that passes through points P(1,2,3)P(1,2,3) and…

A: This is the rough image Point P(1,2,3) and Q(2,3,4) are the points on the plane…

Q: Find a vector that is perpendicular to the surface 4e^{(z-1)}+x^{2}y=xyz at the point (−1,−2,1).

A: Given the surface :

Q: Find the distance between two lines (L1: x=3t-1, y=t+6, z=2t+3 and L2: x=2t+6, y=2t+11, z=-t+3)…

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Q: Find the plane containing the intersecting lines x = -1+t, y = 2+ t, z =1–t; -0 <t < o∞ | L2: x = 1…

A: Find the planes containing the intersecting lines: L1:x=-1+t,y=2+t,z=1-t for all…

Q: Find an equation of the plane tangent to the surface z = x2 - y at the point (2, 1, 3). O A. 4x - 2y…

A: Find an equation of the plane tangent to the surface z= x2 - y2 at the point (2,1,3). Here i…

Q: Find the distance from a point P(x1, y1, Z1) to the plane Ax + By + Cz = D.

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Q: The equation of the plane that passes through the point P(1,0,0) and has the vector n = (0,0, 1) as…

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Q: Find for the point P(x,y,z) on the plane 3x + y – z – 15 = 0 that is closest to the origin.

A: The distance of the point P(x,y,z) from the origin is: d2=x2+y2+z2 Now we have to minimize d if the…

Q: At what point on the curve x = t³, y = 6t, z = t4 is the normal plane parallel to the plane 6x + 12y…

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Q: Let R be the triangle in the xy-plane with vertices (0,0),(0, 1),(1,0). Find C[n(2 – x – y) dA.

A: Given vertices of triangle now we have to find the area as shown below

Q: Find an equation for the plane passing through the origin that is parallel to the tan- gent plane to…

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Q: Find the projection of a on the plane P if a 4 and P has the equation x + y + z = 1.

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Q: Find a parametrization r(t,s) for the plane which contains the point P(-9, 7, 1) and the line…

A: Use plane concept

Q: Find an equation for the normal plane for r(t) at the point (0, 7, –1). Find an equation for the…

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Q: Find m, n ∈  R so that the line r X: (n, 2,0) + λ (2, m, m) is contained in a plane π: x -3y + z = 1

A: The direction cosines of the line, r(x)= (n, 2,0) + λ (2, m, m) are &lt;2, m, m&gt; . The direction…

Q: x(t) Find a plane containing the line y(t) z(t) - 6x - 4y - 5z = - 4 = = = 2 + 4t -1-6t and…

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Q: a) Show that the line I = 0, y = t, z =t where te R a) lies in the plane 6z+4y–4x = 0 b) is parallel…

A: In the question it is asked to solve for the planes having equation given below.

Q: Let P be the plane with equation x-2y+2z =-10. Find four distinct points on P at distance 6 v2 to…

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Q: 12. Find the distance from the point P(0,0,0) to the plane given by x + y +z= 6.

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