orthonormal 3D vectors

Q: Consider the vectors i = (2, – V3, 1) and ū = (-1, v3, 4). Find the orthogonal decomposition of u…

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Q: Compute the new position of the square [A(19,19), B(29,19), C(29,29), D(19,29)] after its rotation…

A: ABCD is a square , we need to rotate it clockwise along with centroid.

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

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Q: Find a nonzero vector orthogonal to the plane through points P(2,1,5), Q(-1,2,3), and R(0,3,3), and…

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Q: Find the vector projection of b = 6î + 3ĵ + 2k onto å = î – 2ĵ – 2k.

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Q: Show that the vectors V1 = ( 1, 1, 2, 4 ), V2 = ( 2, -1, -5, 2 ), V3 = ( 1, -1, -4, 0 ) and V4 = (…

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Q: The vectors a =(1; 4; 2021) and b = (2; -8; 199) are obviously non- %3D orthogonal because the dot…

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Q: Find the image of the vector (1, 1, 1) for the rotation.30° about the z-axis

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Q: Find the matrix that produces the rotation. Then find the image of the vector (1, −1, 1).90° about…

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Q: What is the matrix representing a translation by vector [−1, 2, −1]? What is the matrix representing…

A: The given matrix is -12-1. The rotation angle at 90°. So if the rotation is θ around Y axis is,…

Q: Find a vector orthogonal to both v and u. V = 2i - 2j + k, u = -4i - 4j + 5k -6i - 7j + 7k 6i + 7j +…

A: Given is           v = 2i -2j +k           u = -4i-4j +5k         two vector a & b said to be…

Q: find "a" so that the vectors v=i-ja and w=2i+3j are orthaganal?

A: Given,  v=i-ja and w=2i+3j Two vectors are orthogonal if and only if their dot product is zero

Q: Find the coordinate vector[x],of x relative to the given basis B= {bl,., bn}. --]--[}]--[1] bị = ,b2

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Q: For a C4 axis along z axis, please find the matrix for c, the synmetry opertion on a vector·

A: Given, C4 axis is along z axis . Upon action of C14 symmetry operation, the change with respect to x…

Q: What is the resultant of vectors a and b? ( A ) GL B

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Q: Consider the space P2 and consider the vectors B ={ 1 + 2t +2t2, 3+5t +3t2,-2-3t} and C = {1,t,t2}.…

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Q: Find a vector that is orthogonal to the triangle with vertices P=(1,0,0), Q= (0,2,0), R=(1,1,1)

A: RECALL: Orthogonal vector:  Let us consider to vectors a→ and b→ then , cross product of a→ and b→…

Q: Find out Vector S= { V, V2, V3} is the Basis por R. if VI : ( 3,1,-4), Vz C2,s,6), V3 - C1,4,8) %3D…

A: Here we have to find whether v1 , v2 , v3 are basis of R3 or  not.

Q: Show that the column vectors (1,1,2,4), (2,-1,-5,2), (1,-1,-4,0) and (2,1,1,6) vectors in R are…

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Q: Find the image of the vector (1, 1, 1) for the rotation.120° about the x-axis

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Q: The z-coordinate of the terminal point of the vector v=-5i-19k whose initial point is (-1,-4,-5) is

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Q: Find a vector, v, in component form, that is orthogonal to the plane containing the points P = (4,…

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Q: Find the matrix of the reflection about the line L.

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Q: Find the scalar equation for the plane passing through the points P-(-1. 5.-1. P=(-1, 6, 5), and…

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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: Determine whether the vectors v, = 1 10 and 11 are linearly %3D V3 independent.

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Q: Given the vector u = (4, 1, -6) and a = (1, O, 5). The orthogonal projection of u on a (projau ) is…

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Q: Find the matrix that produces the rotation. Then find the image of the vector (1, −1, 1).45° about…

A: Given  The vector (1, −1, 1) and 45° about the z-axis is

Q: Write the Rodrigues vector and the quaternion corresponding to the rotation matrix - cos(T/3)…

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Q: Find the coordinate vector of v relative to the basis S = {v1, v2, V3} for R3. v = (-11,–17,7) V1 =…

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Q: Find a vector orthogonal to both v and W. v = 3i + 2j + k, w = -5i - 5j - k 3i - 2j - 5k -3i + 2j -…

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Q: Find a vector orthogonal to (0, 1, 7) and (2i – j+ 4k) 11i + 14j - 2k 2i - j+ 11k -j + 28k 4i + 14j…

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Q: Determine whether the vectors a = 2i-3j+ 5k, b 3i+j-2k and c=i-7j+12k are linearly dependent or…

A: “Since you have asked multiple question, we will solve the first question for you. If youwant any…

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

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Q: Find the image of the vector (1, 1, 1) for the rotation.60° about the y-axis

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Q: Consider the four vectors X1 = (0, 0, 0)', X2 = (1, 0, 0)", x3 = (1, 1, 0)", x4 = (1, 0, 1)'. %3D…

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Q: Find the coordinate vector of a -2 with respect to the basis B %3D for R.

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Q: Let u = (-3, -1, 3) and : = (3, 1, 2). Find the vector component of u orthogonal to a. a 3D

A: Since you have asked multiple questions in single request  so we  will be answering only first…

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

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Q: Find the vector W which is of length 6 and oppositely directed to u = (2,-2,1)

A: Given,          The vector w→ which is of length 6 and oppositely directed to u→=<2,-2,1>.

Q: Determine the matrix that produces the pair of rotations. Then find the image of the vector (1, 1,…

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Q: Find the image of the vector (1, 1, 1) for the rotation.60° about the x-axis

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Q: Find the vector form for the geveral selution to the system of equations. X, - X, + Zxg - xy - Xx=-8…

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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 a vector, in component form, that is orthogonal to the plane containing the points P = (5, 2,…

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Q: Find the cross products uxv and vxu for the the vectors u=2i-j-2k and v= i +3j-2k.

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Q: . Find the coordinates of the vector v relative to the ordered basis B. a) B = {x² + 2x +2, 2x…

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Q: Find the cross products uxv and vxu for the the vectors u = 3i-j-2k and v=i+2j-3k.

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Q: Find the orthogonal projection of the vector b =-1 on Nul(A), where -2 -2 3 -10 A = 1 -1 2 3 1 -3 3…

A: For the solution follow the next steps.

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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