2) Find the vector from the origin to the center of the sphere 2x² + 2y² + 2z2 + 4x - 4z = 0.

Q: The plane with normal vector (0, – 2, – 4) containing the point (-7,4,-3) has equation Aæ + By + Cz…

A: We are authorized to answer one question at a time, since you have not mentioned which question you…

Q: 1) in triple dot of vectors |(A x B). C = |(CX A). B\, where the vectors A, B, and C are not same…

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Q: 2. Find the volume of the parallelepiped formed by vectors d (-1, 2, 1), 6 = (3, –2, – 1) and T =…

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Q: Find a vector ū that is parallel to the yz-plane and perpendicular to the vector i = (0, 2, 2).

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Q: Find an equation of the plane. the plane through the point (5, 6, 5) and with normal vector 6i + 8j…

A: As we know that the equation of the plane which is passing through a point Px0,y0,z0  and normal…

Q: Find a nonzero vector parallel to the line of intersection of the two planes 3y+4z=−3 and 5x+y+2z=4

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Q: 2. Find the vector, parametric and cartesian equation of a plane that contains the points А(-1,0,…

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Q: Find the distance from the origin to the plane through the point (-6,3, -2) and having 5i - 3j° + 4k…

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Q: Find a unit vector n that is normal to the surface 2z^2−x^4−y^4=1 at P=(1,2,3) that points in the…

A: We have

Q: 2- Are the vectores [4,2,6] and [6, 3, 9] collinear? How do you know?

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Q: what is the parametric and symmetric eqvotions of the line that passes thrs point (4.-3,57 to beth…

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Q: Find an equation of the plane. The plane through the point (2, 9, 6) and with normal vector 7i + j –…

A: Find an equation of the plane

Q: Find an equation of the plane through the point (4, 5, 1) and with normal vector 6i + j - k. Show…

A: The plane passing through a point A(a) with the normal vector n is given by: r·n=a·n where,…

Q: The plane contains the point (2, −1, 6) and is normal to the vector <2, −1, 6>.

A: Given: A plane passes through the point 2, -1, 6 and normal to the vector 2i^-j^+6k^.

Q: The plane contains the point (−2, 3, −1) and is normal to the vector 3i − 2j.

A: Given: point -2,3,-1   and vector 3i-2j

Q: Find the two vectors of length 1 normal to the plane given by the equation 3x – 2y + 4z = 7. -

A: From the plane equation we will get the direction ratio of normal. As the length of the required…

Q: The normal line to the surface x² + 2y² + ² = 25 at the point (1, -2, 4) is parallel to the vector O…

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Q: Find the vector equation for the line of intersection of the planes 3x−2y+2z=1 and 3x+4z=−4

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Q: Find the vectorequationof the line of intersection of the planes  2x-3y–z=5 and x+y+2z=1

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Q: find a vector parametrization for the line with thegiven description. Passes through (1, 1, 1)…

A: To find the vector parameterization for the line that passes through the point (1, 1, 1) and…

Q: s the vector ở = (-1,–2,3) perpendicular to the plane 3x + 6y – 9z + 5 = 0? %3D

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Q: Give a vector parametric equation for the line that passes through the point (–2, 1, –2), parallel…

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Q: Find an equation of the plane. The plane through the point (6, 1, 5) and with normal vector 5i + j -…

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Q: Write the equation of the plane with normal vector n = 4k passing through the point (7, 2, 5) in the…

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Q: Find two different vector parametrizations of the line through P = (5, 5, 2) with direction vector v…

A: Given the points are (5,5,2) and the direction vector v=<0,-2,1>Hence, Vector…

Q: The scalar equation of the plane with normal vector [4, -1, 9] and passing through the point (2, -1,…

A: The scalar equation of the plane with normal vector [4, -1, 9] and passing through the point (2, -1,…

Q: Show that the point 1, - 2, 0 lies on both planes 3x-2y+z=7 and x-4y-2z=9. Hence, find the vector…

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Q: Find an equation of the plane that passes through the point Po(0,2, – 2) with a normal vector n =…

A: Find an equation of the plane that passes through the point p0 (0,2,-2)with a normal vector…

Q: find the vector equation of a plane that contains the intersection line of x + y + z = 1 and x – y +…

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Q: Find the Directional Derivabive of Pary,2)= x-yz'+ at the point CI, -2, 0) in the direcbion of…

A: A scalar function is a rule to associate a number to a particular point in space. The directional…

Q: 4. Determine a vector equation for the plane that is parallel to the xy -plane and passes through…

A: Due to our answering guidelines we can only answer one question at a time, therefore I will be…

Q: 2) Find the vector from the origin to the center of the sphere 2x2 + 2y2 + 2z2 + 4x – 4z = 0.

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Q: Find an equation of the plane. The plane through the point (9, 3, 4) and with normal vector 8i + j…

A: To find- equation of  the plane.

Q: Write the equation of the plane with normal vector n = 4k passing through the point (7, 2, 5) in the…

A: The equation of plane with normal vector (a,b,c) passing through the point p0 =(x0 ,y0 ,z0 ) is…

Q: The scalar equation of the plane with normal vector [4, -1, 9] and passing through the point (2, -1,…

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Q: A vector is 0.888 m long and points in a 205 degree direction. Find the y-component of the vector.

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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: ind a vector orthogonal to the plane containing points (3, 1, 1), (4, 0, 2), (6, 3, 1).

A: Given problem:- Find a vector orthogonal to the plane containing points (3, 1, 1), (4, 0, 2), (6, 3,…

Q: 2. Can three vectors in the xy plane R2, have u v < 0, v w < 0, w u<0?

A: Given that, u, v and w are vectors in XY plane. The dot product of vectors is defined as, if u = a1…

Q: Write the vector A = 2z1-xi + yk in cylindrical coordinates.

A: *concept:- cylindrical co-ordinate = (x, y, z).

Q: 3) Explain why the Cartesian equation 2x– 5y+ 3z = 2 does not describe the plane with normal vector…

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Q: Find the linear equation of the plane through the point (2, −2, 6) and with normal vector j+2k.

A: Explanation of the solution is given below...

Q: Is the line passing through the point (3/2, 1) and slope −2 a hyperplane ? If yes, identify this…

A: Any line in 2D is a hyperplane.  ax+by=c, is a hyperplane (a,b) is called the normal vector  c is…

Q: Write the equation of the plane with normal vector n = (1, 3, 4) passing through the point (3, -1,…

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Q: 2) Find the vector from the origin to the center of the sphere 2x2 + 2y² + 2z2 + 4x – 4z = 0. |

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Q: Consider the plane that goes through the point (4, 1, 3) I to vector (2, 3, 1).

A: It is given that the plane is passing through the point (4,1,3) and orthogonal to the vector (2,3,1)…

Q: Find a vector that is perpendicular to the graph off (x, y) = 3 + 3x−y at (x, y).

A: Given: fx,y=3+3x-y The normal vector to the given graph can be determined by the gradient of the…