Find a set of vectors {ü, ī} in R' that spans the solution set of the equations w - 1 - 2z 1 5w + 2z + y - 2z 0, %3D 0. %3D

Q: Find an equation of the plane that passes through the point P(2, 5, 1) and has the vector n = (1,4,…

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Q: Find an equation of the plane. The plane through the point (1, 7, 2) and with normal vector 4i + j –…

A: Given:   Point : ( 1 , 7 , 2)  Normal vector : 4i + j - k

Q: Find a nonzero vector orthogonal to the plane through points P(2,1,5), Q(-1,2,3), and R(0,3,3), and…

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Q: snip

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Q: Find a unit vector perpen dicular to the plane of the vectors a = (2, -3,1) and b = (1, 2, -4)

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Q: Decompose v into two vectors, v1 and V2, where v is parallel to w and v2 is orthogonal to w. v=i+j,…

A: A vector parallel to w can be obtained from the following formula, v1=v.ww2w and the other vector…

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

A: We need to find a vector parallel to the line of intersection of the planes 2x+3y-z=11 and 4x + 2y -…

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 a nonzero vector parallel to the line of intersection of the two planes – (2x + 3y + z) = -2…

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Q: Find the vector equation of the intersection of the plane x+2y+3z=2 and x+3z=3  r=<  ,  , 0…

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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: Can three vectors in the xy plane, R^2, have u.v<0, v.w<0, w.u<0

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Q: Verify that the two planes are parallel. -x + 6y + 2z = 8 -x + 3y + z = 9 2. Find the normal vector,…

A: Find your answer below

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

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Q: Find volume V(S) of the parallelepiped S in R3 determined by the (3,4,1); v3 following vectors: vị =…

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Q: Find two unit vectors that are parallel to the yz-plane and are orthogonal to the vector 10i – 2j +…

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

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Q: Find an equation of the plane. The plane through the point (2, 3, 6) and with normal vector 8i + j…

A: We will solve the problem.

Q: nd the flux of the vector v=⟨x,y,z⟩ along the surface of the right tetrahedron below.

A: Flux of the vector

Q: The dot product of two vectors X1 y1 y2 and y = X2 Xn Yn ... 18

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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 the vector n= normal to the plane passing through the points (0, -3, 0), (2, -1, 0) and (-2,…

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Q: When decomposing the vector into the sum of two vectors the first is parallel to the other vector…

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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: Two linearly independent vectors in R3 span R2, is that true

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Q: What is the length of the vector whose initial point is (0, 1, -2) and (2, - 2, 3) 35 A. 38 В. V35…

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Q: Find a set of vectors {u, v} in R* that spans the solution set of the equations w - x -y+ 3z 0, %3D…

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Q: Find a vector v→parallel to the intersection of the planes 3x+y+2z=3 and       −(x+2y+4z)=7

A: Vector parallel to intersection of two planes is cross product of the normal vectors of the two…

Q: Find two linearly independent vectors perpendicular to the vector 4 v =

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Q: Find the possible values of x if vectors are j +2k, v =2i + j –- k and w = xi+j - k coplanar: u = i…

A: Given vectors are u=i-j+2k, v=2i+j-k and w=xi+j-k. To find the possible values of x if vectors are…

Q: Find a non-zero vector x perpendicular to the vectors  v= [-3]    And u = [-1]      [11]…

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Q: Two vectors of magnitudes A=3 and B=3v2 are lying on the xy plane as shown in the figure. What is…

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Q: Find a vector x = ( c, d) that has dot products x · r = 1 and x · s = 0 with two given vectors r =…

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Q: Find a vector w perpendicular to both vectors u=2i-j+2k and v=3j-4k w=i+2j-3k w=-2i+8j+6k…

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Q: What can be said about non-zero vectors ū, v and w if (ūxv)· w = 0?

A: Here use the definition of cross product and dot product of 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 a vector v parallel to the intersection of the planes 3x + y + 2z = 3 and – (x + 2y + 4z) = 7.

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Q: Find nonzero vectors u, v, w that are perpendicular to (1, 1, 1, 1) and to each other.

A: Then   -------------(1) Also  --------------------(2)

Q: Find a set of vectors {u, v} in R“ that spans the solution set of the equations 0, 0. w – x – 3z 5w…

A: To find a set of vectors {u,v} in R^4 that spans the solution set of the equations

Q: Realize the Cauchy-Schwarz inequality for the vectors x= ( -1, 2, 4,3), y=(0,-2,1, 4) ∈ R4 and find…

A: I am going to solve the given problem by using some simple algebra to get the required result.

Q: Decompose v into two vectors Vị and v2, where vi is parallel to w and v2 is orthogonal to w. v - -2i…

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Q: Find a set of vectors {u, v} in R* that spans the solution set of the equations w -x-y+ 3z 5w + 2x +…

A: In the question it is asked to write the vector for the given equations. w-x-y-3z=05w+2x+y+3z=0 AS…

Q: Qy: In VĘ CR) find all vectors which are orthegonal to u=(1,-2, 3) uut corath

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Q: Find a set of vectors {u°, v*} in R4 that spans the solution set of the equations w-x-2y+3z=0…

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Q: Find the angle θ between the two vectors.u = (1, −1), v = (0, 1)

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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: Find two linearly independent vectors perpendicular to the vector i = |3

A: to find linearly independent vector perpendicular to vector v→=139 solution let X=x1x2x3 as we know,…

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

A: Answer

Q: Find a nonzero vector parallel to the line of intersection of the two planes 5z – (3x+3y) : 2 and 2x…

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