Find one voctor in R' that spans the intersoction of U and W where U is the xy-plane-that is, U = {(a, b, 0)and W is the space spanned by the vectors (1,1, 1) and (1,2,3).

Q: Find a unit norm vector that is orthogonal to both the vector (1,2, –1) and the line of intersection…

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Q: To compute h, (x) =*,+0,x,+0,*, in vectorized form then: (theta vector size is 1x3 and X is 3x1) (A)…

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Q: Find a linear mapping G that maps [0, 1]×[0, 1] to the parallelogram in the xy-plane spanned by the…

A: A linear mapping G that maps [0, 1]×[0, 1] to the parallelogram in the xy-plane spanned by the…

Q: Find a unit vector normal to the plane containing v=2i+3j-k and . w = -2i - 4j - 3k.

A: Given: v=2i+3j-k  w = -2i - 4j - 3k.

Q: Use Lagrange multipliers to find a vector in 3-space whose length is 3 /3 and whose components have…

A: In the equation ∇g=λ∇f, delta represents partial derivative. A partial derivative is a derivative in…

Q: Find the equation of the plane in xyz-space through the point P=(2,5,5) and perpendicular to the…

A: Given: The point on the plane is P= (2, 5, 5). The plane is perpendicular to the vector n= (1, -4,…

Q: Use Lagrange multipliers to find a vector in 3-space whose length is 8V3 and whose components have…

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Q: Prove that u is orthogonal to v - proju(v) for all vectors u and v in Rn, where u ≠ 0.

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Q: Find a vector function that represents the curve of intersection between the paraboloid 2 z = 4x² +…

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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: Find a linear mapping G that maps [0, 1] x [0, 1] to the parallelogram in the xy-plane spanned by…

A: Consider the given figure with the following conditions:

Q: Use Lagrange multipliers to find a vector in 3-space whose length is 7 V3 and whose components have…

A: By using Lagrange multipliers we have to find a vector in 3-space whose length is 7√3 and whose…

Q: Find a vector that is orthogonal to the plane containing the points. (Orthogonal means…

A: Given points are, P=3,0,1Q=4,-2,1R=5,3,-1 The orthogonal vector n^ will be calculated from the given…

Q: Find a vector v that is perpendicular to the plane through the points А %3 (0, 4, —3), В 3 (5, —5,…

A: Coordinator of the plane is given Find out the vector that is perpendicular to the plane

Q: Find a vector of length 2 orthogonal to the plane 3x – 4z = 5. %3D

A: Here we have to find the vector of length =2 and  orthogonal to the plane 3x - 4z = 5 Let the vector…

Q: Find two vectors of norm 1 that are orthogonal to the vectors u = and v =

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Q: Find a vector function that represents the curve of the intersection of the two surfaces. The…

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Q: The vector a in 3-space of length 3 lying in the yz-plane pointing upward at an angle of 5π/6…

A: let w= aiÌ‚ + bjÌ‚ + ckÌ‚   |w|= a2 + b2 + c2 = 1   W is lying in YZ plane and at an angle of 5π/6…

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 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: Show that except in degenerate cases, (u * v) * w lies in the plane of u and v, whereas u * (v * w)…

A: We will prove that  (u*v)*w=(u.w)v-(v.w)u u*v=ijkuxuyuzvxvyvz…

Q: Find the vector in R° from point A = (x, y, z) to B = (-2, –4, 1).

A: Given points  A  = (x,y,z) B = ( -2,-4,1) To determine the vector in R3 from point A to point B

Q: Find basis for the set of vectors in R'on the line y = nx. Where n=9.

A: Note that ℝ2 forms a vector space over the field of Real numbers ℝ. Let W =x1x2∈ℝ2  : x2 =9 x1 ,…

Q: The initial and terminal points of the vector v are (x1, y1, z1) and (x, y, z). Describe the set of…

A: Concept: The calculus helps in understanding the changes between values that are related by a…

Q: Use Lagrange multipliers to find a vector in 3-space whose length is 9/3 and whose components have…

A: We will use Lagrange Multiplier method to  maximize / minimize a function f(x,,y,z) subject to…

Q: Find a vector v that is perpendicular to the plane containing 3 -() 6 and 0 2

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Q: In each part, use a scalar triple product to determine whether the vectors lie in the same plane.…

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Q: Use Lagrange multipliers to find a vector in 3-space whose length is 6/3 and whose components have…

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Q: ^2

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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: Let v =5j and let u be a vector with length 3 that starts at the origin and rotates in the xy-plane.…

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Q: What is the dimension of the vector space spanned by the vectors v1, v2? v1 = (6, -2, 4) and v2 =…

A: v1 = (6, -2, 4)  v2 = (14, 2,8)  There does not exist any real number c such that v1 = c v2 hence v1…

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: Evaluate The Work Done By The Force Vector, F= (6x^2+3y)I – 15yzj + 10x^2zk From (0,0,0) To (1,1,1)…

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Q: Let p and q be two non-zero vectors. By using the definition of vector product show that pxq =…

A: In the given question, calculate the area of the parallelogram where two sides p and q are given.…

Q: Use Lagrange multipliers to find a vector in 3-space whose length is 4/3 and whose components have…

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Q: Use Lagrange multipliers to find a vector in 3-space whose length is 7/3 and whose components have…

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Q: Find a vector u € R' such that, at the point (2, 1, -1), the function f(, v, 2) =-y + 2a2 + has its…

A: Given, f(x,y,z)=-y3+2x2+z2

Q: Let W Span{u1, u2, u3}. Write y as a sum of a vector in W and a vector orthogonal to W. %3D

A: Orthogonal Decomposition theorem: Let W be a subspace of ℝn. Then each y∈ℝn can be written as,…

Q: Find a linear mapping G that maps [0, 1] x [0, 1] to the parallelogram in the xy-plane spanned by…

A: Given: The maps [0, 1] x [0, 1] to the parallelogram in the XY-plane spanned by the vectors (2, 3)…

Q: Show with the help of the calculation rules for the scalar product for vectors ||x – 2 y|| = ||x||2…

A: The property used here are b2=b·b x·y=y·x cx·y=cx·y=x·cy Consider the left hand side of the given…

Q: Is it true or false that the vector u (3, 3, –3) is a normal vector to the plane -x – y + z + 3 = 0…

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Q: 4. A unit vector orthogonal to A and whose representations are parallel to the yz-plane.

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Q: find two distinct vectors on the line belonging to the intersection of the hyperplanes: Xi+ 2x2 - X3…

A: We need to find two distinct vectors on the line belonging to the intersection of the hyperplanes

Q: 3. Show (using the concept of vectors) that the area of the triangular region with vectors u 1 and v…

A: Given that, The vectors u and v are the vectors of the adjacent sides of the triangular region.…

Q: Use the triple scalar product to find the volume of the parallelepiped having adjacent edges given…

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Q: Show that (x, y) = 4x1y1-7x2Y2 for vectors x = (x1, x2) and y = (V1 Y2) in R2 defines an inner…

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Q: Use Lagrange multipliers to find a vector in 3-space whose length is 6/3 and whose components have…

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