Find a unit vector that is orthogonal to both [0, 1, 1] and [1, 0, 1].

Q: Find two vectors of norm 1 that are orthogonal to the vectors u = (2,−3,4) and v = (3,1,−5)

A: The cross product of two vectors is perpenducular to both of the vectors. The cross product of the…

Q: Find a unit vector that is orthogonal to both u = (2, – 10, 8) and v = (4, 6, – 8).

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Q: Find a unit vector orthogonal to both u = (1, -2, 1) v =(2, 1, 0)

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Q: Find the two unit vectors orthogonal to both a = (3, 1, 1) andb = (−1, 2, 1).

A: Given: a=3,1,1 and b=-1,2,1

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: Find the unit vector that has the same direction as vector v that begins at (1, 4, 10) and ends at…

A: We will find the unit vector that has the same direction with the given vector v in the following…

Q: Find a unit vector in the xy-plane that is orthogonal to

A: Here given vector as a=123 Consider a vector as b=25-150 Now find the dot product of vector b to…

Q: Find the vector with length V17 and same direction as = (7,0, -6).

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Q: Find a vector that is orthogonal to v =〈1, 2, 1〉 but not to w =〈1, 0, -1〉

A: Given: Find a vector that is orthogonal to v =〈1, 2, 1〉 but not to w =〈1, 0, -1〉

Q: Find a unit vector in the direction of u = (3, 4, 5).

A: Given vector, u=3, 4, 5

Q: Find a vector of length 5 that is orthogonal to both vectors ⟨4,−1,0⟩ and ⟨−3,2,−1⟩

A: The vector orthogonal to two vectors u,v is = ± (u×v)/ |u| |v| Here u =  ⟨4,−1,0⟩ , v =…

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

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Q: Find a unit vector perpendicular to plane PQR determined by the points P(-3, 3, -4), Q(4, -1, - 23),…

A: Given query is to find unit vector perpendicular to PQR.

Q: A vector whose initial point is at the origin is called a/an________ vector.

A: Consider the given: A vector whose initial point is at the origin is called a/an________ vector. A…

Q: 3 Determine the unit vectors that are nernendicular to A - and R -

A: Perpendicular vectors

Q: Find a nonzero vector orthogonal to the plane through the points P, Q and R if P(1,0,0), Q(7,8,0)…

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Q: Find two unit vectors orthogonal to both u→=⟨3,4,1⟩ and v→=⟨0,3,3⟩.

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Q: Find a unit vector perpendicular to the plane of P(1, -1, 0), Q(2, 1, -1), and R(-1, 1, 2) .

A: Given P(1, -1, 0), Q(2, 1, -1), and R(-1, 1, 2) .

Q: Find unit vectors that satisfy the stated conditions.

A: I have provided this answer with full description in step-2.

Q: Find the unit vector in the direction of v = (3, −1, 2), and verify that this vector has length 1.

A: Vector v = (3, −1, 2) Such that,

Q: Find two unit vectors orthogonal to both (1,-1,1) and (1,0,3)

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

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Q: Find a unit vector that is orthogonal to both u and = (-8, -6, 4) v = (17, -18, -1)

A: In this question we will use basic of calculus i.e vector calculus. We will simply find the cross…

Q: Find two vectors of norm 1 that are orthogonal to the vectors u = (2,1, -4,0), v = (-1,-1,2,2), and…

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Q: Find two vectors that are orthogonal to ⟨0, 1, 1⟩ and to each other.

A: Vector: Let the two vectors are v and w. We have to find the two vectors which are orthogonal to…

Q: Find a vector that is orthogonal to both v = (1, –2,3) and w = (2, 1, –1).

A:

Q: Find the length of the vector.v = (0, 1)

A: If Vector V = (V1,V2, V3) then the length of Vector ||V|| = (V1)2+(V2)2+(V3)2

Q: vector that is orthogonal to both u and v. u  =      v  =   <15, −18,

A: Given vector u→=-8,-6,4                    v→=15,-18,-1Now , u→ x v→=i∧j∧k∧-8-6415-18-1u→ x…

Q: Find a vector of length 3 pointing in the same direction as .

A: Find a vector of length 3 pointing in the same direction as 4,-3,-4

Q: Find a vector parametrization of the line through P = (0, –8, 7) in the direction v = (7, 0, 0)

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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: Find a unit vector in the direction of u = (5, 3, 2).

A: Given vector is u=(5,3,2) Find a unit vector

Q: Find the two unit vectors orthogonal to both a = (4, 1, 1) and b = (-1, 4, 1).

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

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Q: Find a unit vector that is orthogonal to both u = (2, -8, 6) and v = (4, 10, -6).

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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: Find a vector that is oppositely directed to v = with a length of V3

A: We have to find the vector by given data

Q: Find the magnitude of the projection of (- 1, 2) onto the vector (3, 5)

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Q: What is the resultant of vectors a and b? (

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

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Q: Find a vector orthogonal to the vectors and

A: This problem belongs to vector section and we solve this using dot product concept

Q: Find the unit vector that has the same direction as vector v that begins at (0, -3) and ends at (4,…

A: If a vector is of the form ai^+bj^   then its unit vector along the direction v is written as…

Q: Show that the vectors ( 1, 0,1) ; ( -1, 2,3) and (0, 1; -1) spans R³

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Q: Find a unit vector that is orthogonal to both u = ⟨2, −10, 8⟩ and v = ⟨4, 6, −8⟩.

A: The given vectors are u = ⟨2, −10, 8⟩ and v = ⟨4, 6, −8⟩. Compute the cross product of u and v as…

Q: Find the coordinate vector for the vector v = (3,4,3) relative to the basis S={(3,2,1), (-2,1,0),…

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Q: Find a unit vector in the xy plane that is orthogonal 2 to 4 6

A: We have to find the unit vector.

Q: Find the two unit vectors orthogonal to both a = (4, 1, 1) and b = (-1, 4, 1). %3D

A: