How do you find out the projection of a vector u on a vector w

Q: Find a vector v with initial point vector in the direction of v. Enter your answers in i, j, k…

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Q: Find a unit vector orthogonal to both u and v. (-3, 4, –2) (-1, 1, 0) u = V = 2 2 1 3' 3' 3

A: Given two vectors u and v, then the vector that is orthogonal to both u and v is their cross…

Q: Find the length of the vector. v = (0, 2) ||v| = %3D

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Q: Find the projection of vector ū = -i+ 5j + 3k onto the vector i = -i +j- 3k? %3D

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Q: What is the zero vector?

A: We have to define

Q: How are a vector and a scalar different?

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Q: Find a unit vector u in the direction of v. Verify that ||u|| = 1. v = (-6, 6)

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Q: Find the magnitude of the projection of (- 1, 1) onto the vector (- 1, 5) Round your answer to at…

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Q: (a) Using Gaussian elimination, find a vector v such that

A: As per our guideline is multiple questions are posted we are supposed to answer only the first one.…

Q: Are vectors v = ⟨ − 2 , − 3 ⟩ and u = ⟨ 6 , − 4 ⟩ orthogonal? Yes or No:

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Q: Determine all vectors v that are orthogonal to u.u = (2, −1, 1, 2)

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Q: snip1

A: orthogonal to u means the dot product of the vectors should be zeroso v.u=0xy.31=03x+y=0from here we…

Q: Find the vector projection of b onto a when b = (4, 3), a = (2, –1). 7 (2. –1) 1. vector proj. - 7…

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Q: The scalar projection of vector A onto another vector B will be the negative of that scalar…

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Q: Explain when a projection vector is negative, positive, or zero.

A: This question is based on dot product of two vector.

Q: Find a unit vector orthogonal to both u and v.u = (−4, 3, −2) v = (−1, 1, 0)

A: Given u→=(-4,3,-2)v→=(-1,1,0) unit vector orthogonal to both u and v is gruen by     u→×v→‖u→×v→‖

Q: What is the vector projection of a vector u onto a vector v? Give an example of a useful application…

A: Consider the given statement of the question,The vector projection is the vector produced when one…

Q: Find the length of the vector a %3D

A: The length of a vector x→=abc is given by the equation; ||x→||=a2+b2+c2

Q: b) Give an example of 5 linearly independent vectors in R*, or explain why it is impossible to do…

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Q: Find the projection of vector A=(6,7) along vector B=(1,4).

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Q: Find the magnitude of the projection of (8, – 2) onto the vector (4, 7)

A: Wr have to find the magnitude of the projection.

Q: Give an example of a non zero vector that is perpendicular to (5,7,4)

A: We know that "two vectors are perpendicular to each other if and only if their dot product is zero"…

Q: Calculate a projection of vector B on A and prophecy of vector A on B. A = 4i - 3j + 2k.     B = 3i…

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Q: Consider the vector v = ⟨v1, v2, v3⟩. What is the meaning of arccos v2 / II v II = 30°?

A: Consider the vector v=v1,v2,v3 Use the dot product rule: v·j=v×jcosθ=vcosθ where θ is the angle…

Q: Compute the curl of the vector fie

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Q: Find the length of the vector. v = (-2, 0, 5, 1) %3D ||| M = %3D

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Q: What role does the curl of a vector play in an application?

A: We have to write the curl of a vector play in an application.

Q: What is the vector projection of X = (7, 0, – 3) on ỹ = (-1,3,3)? Answer:

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Q: Find the vector component of the vector U orthogonal to a: и %3D (4, —1,2) and a %3D (1,3, —2).…

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Q: How does translation T along vector AB affect the points in the plane?

A: Some information in the question is missing.

Q: Find a unit vector parallel to the vector a´. a'= (-2,3,–1)

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Q: Find a non-zero vector perpendicular to

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Q: For vectors ā = (2,4,-1), b =(-1,3,2), calculate the vector projection of b on ā. %3D

A: Vector projection of b→on a→=(a→.b→)a→Consider  a→.b→=(2×(-1))+(4×3)+((-1)×2)…

Q: Find a Vector ū: non zero Vector perpendicular to the

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Q: A vector orthogonal to the plane through the points (-1,0,0), (0, 1, –-2), (2, 3, 4) is O O O O

A: I have append the formula in solution part

Q: Find a unit vector u in the direction opposite of (-9,–2, –1). u =

A: Given vector is  -9, -2, -1

Q: Determine the vector projection of the vector (5,0, 7) on the vector (–1,3,4).

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Q: Let a = . Find a unit vector in the direction of a

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Q: Explain how to find the unit vector in the direction of any given vector v.

A: To find the unit vector in the direction of the given vector v, divide the vector v by its…

Q: . Let x and y be two orthogonal vectors. Then prove that

A: If x is any vector then Euclidean norm or 2-norm is denoted by ||x||2 and is given by  ||x||2 =…

Q: 2. Find the vector projection of u along v. u = (2,1,3), v=(-2,3,2) V

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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: 1. what is the basic concept of a vector?

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Q: Find a non-zero vector u perpendicular to the vector u =

A: If  A non zero vector is perpendicular to anather vector then their dot product is equal to zero.

Q: Determine whether the vector v = 8 is spanned by the vectors and 3 or not.

A: Given three vectors and we have to find if  v=789 is spanned by111 and 123

Q: Find the length of the vector. v = (5, 0, 3, -2) %3D ||v|| = %3D

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Q: A vector orthogonal to the plane through the points (-1,0,0), (0, – 1, –2), (2, 3, 4) is O O O O

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Q: Describe a unit vector in R^3 with the same direction as <1,0,7>

A: Consider the given point vector

Q: A vector orthogonal to the plane through the points (-1,0,0), (0, –1,-2), (2,3, 4) is O O O O

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