Let u = (4,-1,-1) and v= (2,-2, 2x + 1) be two vectors in space. Find alle ER such that u and v are orthogonal. Find all r R such that |u| = |v| Find the area of the parallelogram determined by u and v. Express your answer in terms of x. (i) (ii)

Q: Given two non-zero vectors a and b such that abs(a+b)=abs(a-b), find the value of a*b (dot product…

A: Given Two non-zero vectors a and b such that  a+b=a-b            ...........1 The dot product of and…

Q: Find vectors u and v whose initial and terminal points are given. Determine whether u and v are…

A: The u vector can be computed as: u=6-1i+11-1ju=5i+10j

Q: The nullspace of A = the values of i and j. i= j= -6 9 -3 -4 6 321 can be written as the span of the…

A: Let A be a matrix of order m*n , then  The null space of A is defined as Nul(A)={ x in Rn : Ax=0 } .

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Q: et V₁ = (1, -2,-2), V₂ = (0, -1, -2), V3 = (2, -4,-5). re the vectors 1, 2 and 3 linearly…

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Q: a. Write the vector (23,-12, -19) as a linear combination of a₁ = (3, -2, -1), a2 (2, -3, -1) and ã3…

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Q: For the given vectors a and b, find the cross product a x b. (2, 0, -3), b = (2, 1, 0) a x b = %3D

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Q: Find the cross product of the vectors a=⟨2,3,−2⟩ and b=⟨−3,−6,−4⟩. Select one: a. ⟨0,2,−3⟩ b.…

A: a*b = <-24,14,-3> option 'e' is correct

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Q: (b) 4x Find any values of x such that the vectors 3 and are parallel X-1 to each other.

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Q: 98. Determine whether the vectors AB and PQ are B(-2, 2, 0), where A(1, 4, 1), equivalent, P(2, 5,…

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Q: Consider the vestun . il 1:= V2: V3: and u where a E R. (a) For which values of a is the span(v1,…

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Q: Find a complex vector d so that if F{(fo, ƒ1, ƒ2 ƒ3)} = ċ then F{(−fo, − ƒ₁, 0, 0)} = č ® ā.

A: According to the given data, find the vector d:

Q: Consider the parallelogram with vertices A(-3, 0), B(-1, 3), C(5, 2), and D(3, -1) Find AB and AD,…

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Q: The zero vector 0 = (0, 0, 0) can be written as a linear combination of the vectors v., v, and v…

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Q: Let a = (-2, 0, 5) and b = (-3,- 2, 4). Find the angle between the vectors (in degrees).

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Q: Find the vector expression for the line that is the intersection of the planes 3x−3y−2z=−2 and…

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Q: a, b, and c are vectors. Then the expression axc+bxa is (a) Meaningless (b) A vector collinear with…

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