Find the scalar and vector projections of b onto a, where a = (-1,1,2) and b = (-4,5,8).

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: The vectors u=(1,-2,1), v=(3,0,-2) and w-(5,-4,0) are: O not coplanar coplanar

A: We can check whether the three vectors are co planar  or not as below

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Q: Find the coordinate vector [x]gof x relative to the given basis B= {b1,., bn}. -[-]»= [-{]==(:)

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Q: Determine a vector that is orthogonal to both (1, 2, -1) and (3, 1, 0).

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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

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

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Q: If a vector is multiplied by a positive scalar, how is the result re-lated to the original vector?…

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Q: Determine a vector that is orthogonal to both (1, 4, −1) and (5, 1, 0).

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Q: Solve numerically for The scalar projection of vector u onto v

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

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Q: What is the scalar projection of á = (1,0, 1) onto b = (0, 3, 4)?

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

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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: Find the scalar and vector projections of b onto a, where a = (2, −2, 1) and b =  (IMAGE)

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Q: 2- Are the vectores [4,2,6] and [6, 3, 9] collinear? How do you know?

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Q: Project the first vector orthogonally into the line spanned by the second vector. 2 3 -2

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Q: Find the scalar and vector projections of b onto a. a = b =

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Q: Find the scalar and vector projections of b onto a. 3i - j + 6k, b = j+ k 2 compab = 46 (3i-j+ 6k)…

A: Given a=3i-j+6k    b=j+12k

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

A: The given vectors are u=(0,1,1) & v=(1,0,1).

Q: Find the scalar and vector projections of b onto a, where a=⟨−1,1,2⟩ and b=⟨−1,5,4⟩

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Q: The terminal point of the vector v = 3i +5j – 4k with initial point (2, –1, 4) is

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Q: Decompose the vector ¯b = ⟨1, 0, 4⟩ into its projection proja¯(¯b) and its orthogonal component…

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Q: Show that the vectors (1, 1, 1), (1, 2, 3) and (3, 3, 4) are linearly independent?

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

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Q: Find the orthogonal projection of the vector onto the vector .

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Q: Find the scalar and vector projections of b onto a. a = (4,7,-4) b =(4,-1, 1)

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

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

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: 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: 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…

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Q: Find the scalar and vector projections of b onto a, where a = (-1, 1, 2) and b = (-2,7,2). 1. comp,…

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Q: Find the scalar and vector projections of b onto a. = (3, –6, –2), b = (3, 3, 2) a

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Q: Find the scalar and vector projections of d = (4, 2, –5) on b = (3, –1, 6).

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

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Q: Find the scalar and vector projections of b onto a, where a = (1, 2) and b = (-4, 1). 1. comp, b 2.…

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Q: Find the scalar and vector projections of b onto a, u

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Q: Find the scalar and vector projections of b onto a. a = 3i - j + 6k,     b = j + (1/2)k compab =…

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Q: Find the scalar and vector projections of b onto a. а - (-4, -3), ь - (6, 0) compab projąb

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Q: Find the scalar and vector projections of b onto a. a = (-3, -6, 2), b= (3, 2, 1) compab projb=

A: Given a→=−3,−6,2 and b→=3,2,1 We have to find the scalar and vector projection of b→ onto a→. The…

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 the scalar AND vector projections of a onto b where a=(0,1,-2) and b=(-1,0,3)

A: Given , a = (0,1,-2) and b = (-1,0,3).

Q: If a vector is multiplied by a positive scalar, how is the result related to the original vector?…

A: Solution:- If a vector is multiplied by a positive scalar, how is the result related to the original…

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

A: Let X=x,y,z,t be the vector that is orthogonal to u= (2, 1, - 4, 0), v= (-1, - 1, 2, 2) and w= (3,…

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

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Q: Use a dot product to determine whether the vectors u = ⟨1, 2, 3⟩ and v = ⟨4, 1, -2⟩ are orthogonal.

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Q: Find the scalar and vector projections of b onto a, where a = (1,2) and b = (-–9, 1). %3D 1. comp, b…

A: We have to e the magnitudes of thr given vector first.

Q: Find the scalar and vector projections of b onto a. (4, 7, -4) ь 3 (3, -1, 1) a

A: a=4, 7, -4, b=3, -1, 1 1. Scalar projection of b onto a is Proj ba. Proj ba=b·aa          =3, -1,…