Find constants a, b, c such that  G( u, v) = ( u + av, bu + v, 2u - c) parametrizes the plane 3x - 4 y + z = 5. Calculate Tu, T v, and N(u, v).

Q: Find parametrizations for the lines in which the planes 5x - 2y = 11, 4y - 5z = -17

A: Given: The given two planes  5x-2y=11 and 4y-5z = -17 are intersects.

Q: Show that the points A = (1, 2), B = (1,0), and C = collinear and express P = (-7,0) in barycentric…

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Q: Find the trace of the plane in the given coordinate plane.3x − 9y + 4z = 5,  yz

A: The trace of the plane in yz plane is obtained by substituting x=0 in the given equation of the…

Q: Find the vector equation for the line of intersection of the planes 5x +y-3z= -3 and 5x + z = -1 r =…

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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 the scalar equation of the plane that contain the line 7 = [2,1,7] + t[0, 1, 0], t e R and is…

A: Here we will find out the required plane.

Q: Determine the parametric equation of the plane that contains the line y-3 *+2-³-² and the point…

A: Virtual find the standard form of the plane then by satisfying the parametric values we will…

Q: Let y = x² be a parabola in the xy-plane parametrized by r(t) = (t,t², 0). What are the vectors T, N…

A: Solution is given below:

Q: Find the symmetrical point of point P(-1,-3,5) with respect to the plane D:3x-2y+z+6=0

A: Point P(-1,-3,5)  plane D:3x-2y+z+6=0

Q: Determine the equation of the tangeht plane f(x, y, z) = x² – 3zyz + 5y at the point (2, 1, 1). O a.…

A: Given:- F(x, y, z) = x2 -3xyz+5y To find:- Equation of tangent plane at point(2, 1,1)

Q: Find the scalar equation for the plane passing through the point P=(4, -5, 3) and containing the…

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Q: Find the equation of a plane that is perpendicular to the vector 3 i - 4j+ 5k and passing through…

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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: Find the trace of the plane in the given coordinate plane.3x − 9y + 4z = 5,  xz

A: Let the plane P whose equation is:                                          3x-9y+4z=5…

Q: Find the vector equation of the line of intersection of the planes x+y+z=1 and x+2y+2z=1.

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Q: Give a scalar equation for a plane at distance 9 from the plane P with equation -2x-2y+z = 4.

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Q: Find a vector parametric equation for the ellipse that lies on the plane 5y−3x+z=9 and is inside the…

A: Given that: 5y-3x+z=9 Let x=u cos v, y=u sin v So z=9+3x-5y  =9+3u cos v-5u sin v

Q: Let M be a plane with the following properties: • M contains the point with coordinates (1,1,-1) ()…

A: since plane is passing through the point (1,1,-1) and orthogonal to the vector 200

Q: Find the angle between the two planes 3x + 2y − z = 7,  x − 4y + 2z = 0 and find a set of parametric…

A: Known fact: The angle between two planes a1x+b1y+c1z+d1=0  and a2x+b2y+c2z+d2=0 is given by…

Q: Find a scalar equation of the plane containing the line x = 4+ 5t, y = 5+3t and z = 6+ 4t the point…

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Q: Find an scalar equation of the plane containing the line x = 2 – 4t, y = 4 – 5t and z = 5+t and the…

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Q: Let M be a plane that contains the point with coordinates (-2,-2,-1) and is orthogonal to the vector…

A: Let M be a plane that contains the point with coordinates -2, -2, -1 and is orthogonal to the vector…

Q: Find the parametric equations for the line through the point of intersection of the lines L1:x = 2 +…

A: In line L1 and L2  't' is used as parameter but don't confuse with it. Different different line we…

Q: Find the scalar equation of the plane that contains the line x+1 -3=. and is parallel to x+2=+4_:+2…

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Q: Consider the plane P with the Cartesian equation 7x+5y + 5z = 33. a) Express the above Cartesian…

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Q: Write the scalar equation of the plane. a) perpendicular to the line [x, y, z]=[1 -2, -3]+t[5, – 4,…

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Q: Find the angle between the two planes −2x + y + z = 2,  6x − 3y + 2z = 4 and find a set of…

A: The given planes are −2x + y + z = 2  and  6x − 3y + 2z = 4 . Obtain the angle between them as…

Q: Find constants a, b, c such thatG(u,v) = (u + av,bu + v, 2u − c)parametrizes the plane 3x − 4y + z =…

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Q: Let M be a plane with the following properties: • M contains the point with coordinates (1,1,-1) ()…

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Q: Find a scalar (Cartesian) equation of the plane that contains the origin and the point  (2, -3, 2)…

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Q: Find the vector equation for the line of intersection of the planes 5x + 4y + 5z = 1 and 5z + z = -4…

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Q: Find a scalar equation of the plane that contains the linex = 1 + t, y = 2 − t, z = 4 − 3tand is…

A: Given,The plane that contains the line x = 1 + t, y = 2 − t, z = 4 − 3t.So, we can say that the…

Q: 12. a. Use vectors to show that the distance from P;(x1, Y1, Z1) to the plane Ax + By + Cz = D is…

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Q: Find the vector equation that represents the curve of intersection of the paraboloid z = 4x² + y²…

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Q: Is it possible to find a plane perpendicular to both i and j? Explain why.

A: The objective is to find a plane perpendicular to both i and j, if possible.

Q: Find the angle between the two planes 3x − y + z = 7 ,  4x + 6y + 3z = 2 and find a set of…

A: Given, two planes 3x − y + z = 7 ,  4x + 6y + 3z = 2  we have to find the angle between the two…

Q: Which of these describes a parametrized line perpendicular to the plane 3x + 2y + z = 15? A) (2 +…

A: The direction ratio of the normal vector to the plane is (3, 2,1 ) So the perpendicular line to the…

Q: Consider the following equation of a plane in R³: -3z – 2y – 3z = -2 Convert your plane to vector…

A: Find the vector parametric form of the plane: -3x - 2y - 3z = -2

Q: Find an equation of the plane through the origin that is parallel to the plane 5x – 4y + 6z + 10 =…

A: Here we have to find the equation of a plane.

Q: Find an equation for the plane that passes through the point (1, 2, 3) parallel to u = 2i + 3j + k…

A: Given:u = 2i + 3j + k and v = i - j + 2kFirst find cross product

Q: Find parametrizations for the line in which the planes 3r- 6y – 2z = 3, and 2x+y-2z = 2 intersect.

A: Given Equation of planes 3x-6y-2z=3 and 2x+y-2z=2

Q: Find an equation of the plane containing the line a = 3t, y = 2 – 4t, z = 1+t and parallel to…

A: We have to find the equation of the plane containing the line x=3t, y=2−4t, z=1+t and parallel to…

Q: Give a scalar equation for a plane at distance 9 from the plane P with equation -2x+y-2z = 3.

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Q: Find the value of d in the equation of the plane ax+by+cz+d=0 passing through the point P(3, 1, -2)…

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Q: Determine the scalar equation of the plane that passes through (5, -5, 5) and is perpendicular to…

A: Here we will find the required equation of the plane,

Q: Write the parametric and scalar equations of the plane given its vector equation [x, y, z] = [4, 3,…

A: Parametric equation is simple: x = 4 + 2s + 6t y = 3 + s + 6t z = -5 + 4s - 3t

Q: Find a vector parametric equation for the ellipse that lies on the plane z (x + 2 - cylinder x + y =…

A: Dear student. You have posted many parts, according to the policy we will answering the first part.…

Q: Find the vector equation for the line of intersection of the planes x – 5y + 2z = 1 and æ + z = 1 |…

A: To find the vector equation of the line of intersection of given planes.

Q: perpendicular

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Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.