Identify the surface with the given vector equation. r(u,v) = (u + v)i + (3- v)j + (2 + 4u + 6v)k a. circular cone b. plane c. hyperbolic paraboloid d. circular paraboloid e. circular cylinder

Q: Consider the planes 5x + 2y + 3 = 1 and 5x + 3 = 0. (A) Find the unique point P on the y-axis which…

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Q: Consider the planes 5x+ 5y+ 3z = 1 and 5x + 3z = 0 (A) Find the unique point P on the y-axis which…

A: a) The y-axis has x and z values of 0. Note that that immediately works for the second plane5x+3z =…

Q: Find a vector normal to the plane with the given equation.9x − 4y − 11z = 2

A: Our Aim is to find a vector normal to the plane with the equation given below:-9x-4y-11x=2 -(i)

Q: Write a vector of magnitude 5, parallel to the plane 3x + 4y + 5z = 10 and perpendicular to the…

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Q: Given Ā =,B = and C =. Find: a) the scalar projection of B onto C – À b) a unit vector ū in the…

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Q: Find a vector parametrization of the line through P = (3, –8, 5) in the direction v = (-2, 0, 3)…

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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: Let r(t) =(t, 4/3 t3/2, t2) Find the equation of the osculating plane at the point correspondingto t…

A: Given that, rt=t, 43t32, t2rt=t, 2t33, t2

Q: Find the orthogonal projection of v = i + j + k on b = 2i + 2j,and then find the vector component of…

A: We have given vectors V=i^+j^+k^ and b=2i^+2j^ Vector component V of  along b…

Q: Verify that 2j+k is perpendicular to the plane I7, Find a vector perpendicular to the plane II, Find…

A: Given that the plane Π2 contains the point O, A and B and the plane Π3 contains the points O, A and…

Q: Find the component form of v, where u = 3i - j and w = i + 3j. v = u + 3w Sketch the vector…

A: We have to solve

Q: Find the vector equation for the line of intersection of the planes x + 4y + z = -5 and x + 4z = 0…

A: Here we have to find the vector equation for the line of intersection of the planes x+4y+z = -5 and…

Q: Find two unit vectors that are normal to the given surface at the point P. z + x = z?;P (3,5, 1) V y…

A: Given The equation of the surface is  z+xy-1=z2 and a point P(3,5,1) on this surface. To find a unit…

Q: Given the vector u (5, – 2), find the magnitude and - angle in which the vector points (measured…

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Q: Consider the planes 5x + 3y + 5z = 1 and 5x + 5z =0 a) find the unique point p on the y-axis which…

A: given planes  5x + 3y + 5z = 1 and 5x + 5z =0

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

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Q: Consider the following plane. 4x + 8y + 12z = 12 (a) Find the coordinates of three points P, Q, and…

A: NOTE: Refresh your page if you can't see any equations. . divide both sides by 12

Q: What is equation of the plane passing through the point A(2, 1,3) and parallel to the vectors a = j-…

A: We have to find the equation of plane passing through point A(2,1,3) and parallel to vectors…

Q: Evaluate 1+ x° + y°dS, where S is the helicoid with vector equation т(и, и) — 0 <u < 3, 0 < v< T

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Q: Find the vector equation for the line of intersection of the planes 32 + 2y :0 ánd 3* + ,0 ) +t(6, r…

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

Q: Find a vector normal to the plane with the given equation. 2x + 8y + 9z = 3 n =

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Q: Consider the planes 5x+2y+4z=15x+2y+4z=1 and 5x+4z=0  (A) Find the unique point P on the y-axis…

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Q: Find a vector perpendicular to the surface: 5zy = a? +y 28 Enter you answer in the form . 15 at the…

A: Gradient of F(x, y, z) at a point is perpendicular to the surface F(x, y, z).

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: 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: For the given vector function below, find the equation of the plane that contains the osculating…

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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: Find the point where the graph of the vector equation r(t) = ⟨2 − 3t, −2 − t, 2 + t⟩ intersects the…

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Q: Find the coordinates of the point P on the line and a vector v parallel to the line x = 3t, y = 1 –…

A: Given parametric equation of line x=3t, y=1-t, z=3+5t

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: Evaluate 1+ x? + y?dS, where S is the helicoid with vector equation r(u, v : 0 < u < 3, 0 < v < 2T

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Q: 1.20. Given the plane 4x +3y +2z = 12, find the unit vector normal to the surface in the direction…

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Q: Consider the line l in R³ given by the parametric vector equation 3 1 -2 -1 and the plane described…

A: Given that the line l in R3 given by the parametric vector equation and the plane described by the…

Q: b) Find the center and radius of the sphere x+y+z6x+4y-10z+25%=D0. C) Compute a ·b, axb, and…

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Q: (a) Find a vector n perpendicular to the plane z = 8x + 9y. (b) Find a vector v parallel to the…

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Q: Evaluate / V1+ x² + y°dS, where S is the helicoid with vector r(u, v) 0 <u < 3, 0 < v< T

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Q: The unit vector normal to the plane 2x + 3y + 6z = 7 is

A: The given plane is 2x + 3y + 6z=7. The unit normal vector to fx,y is defined as n=∇F∇F. The normal…

Q: e part of the plane with vector equation r(u, v) = (4 + v, u – 3v

A: Here we have to find the area of the part of the plane with vector equation r(u,v)=4+v, u-3v,5-4u+v…

Q: Find the component form of the unit vector obtained by rotating the vector (1.0) 210°…

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Q: Given the planes 3x – 6y – 2z = 15 and 2x + y – 2z = 5 anser the following. (a) Find a vector…

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Q: Evaluate 1+ x² + y*dS, where S is the helicoid with vector equation r(u, v) 0 < u < 2, 0 < v < 2T

A: Given ∬S1+x2+y2dS where S is the helicoid with ru,v=u cos v, usin v, v, 0≤u≤2, 0≤v≤2π. Since ru,v=u…

Q: Find the vector equation that represents the curve of intersection of the paraboloid z = 2x² + y²…

A: Given: Let us take x = t. So, we get y=t4  and  z=2t2+t42=2t2+t8.

Q: Find the vector equation that represents the curve of intersection of the paraboloid z = 4x +y and…

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Q: Find the vector equation that represents the curve of intersection of the cylinder a? + y = 25 and…

A: Given equation of cylinder is, x2+y2=25

Q: Find the velocity, acceleration, and speed of an object with position vector r(t) = (Vi, 4 + Vi,…

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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: The part of the plane with vector equation r(u, v) = (u + v, 2 – 3u, 1 + u – v) that is given by 0 <…

A: This is a problem of surface integral.

Q: perpendicular to the plane formed by the vectors w1 = [1 2 1] and w2 = [2 2 3], with the z axis

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Q: Evaluate 1 + x2 + y?dS, where S is the helicoid with vector equation r(u, v): 0 < u < 2, 0 < v < T

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