Compute the result of counterclockwise rotation of a vector a = absin (a) 81 ∞as 23 by an angle = ³.

Q: What is the scalar projection of vector a given by (a₁,a2,a3) in the direction of vector b given by…

A: We have to find the scalar projection of a in the direction of b.

Q: Compute the orthogonal projection of v= 7 onto the line through 4 2 and the origin.

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Q: state a vector with all non-zero entries which is orthogonal to v⃗

A: Given v vector  Let w vector be orthogonal to v vector  Then w vector . v vector = 0

Q: The projection of the vector 5î + 5ĵ – 5k onto the vector –4î + 2ĵ – 4k. | |

A: We have to find out

Q: 1. Find the vector component of the vector ū (-3, 6, 2). [28, 63, 0] in the direction of = %3D

A: We have to find vector component of u =[28, 63,0]  along the direction v=[-3, 6,2] Vector component…

Q: Compute the orthogonal projection of v = proj, (v) = -5 onto the line L through -4 and the origin. 6…

A: Introduction:  The vector projection of a vector a on (or onto) a nonzero vector b, sometimes…

Q: Consider the basis B of R² consisting of vectors (-1, 2) and (-6, -3). Find x in R² whose coordinate…

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Q: y = (−3, −2, −1, 5) and 4 5 2 1 3 0 3 2 2. 1 A= 2 -1 * REQUIRED 18. Compute the resulting vector of…

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Q: Let m (1, 2, 3) and n (5, 3,-2). Find the vector projection of m onto n, that is, find proj- m. You…

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Q: (x.yız) (x,9e)x4か t. 22 P( 3-1,0) けこくりん)2

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Q: If ū = 2î – î and w = î + 2ĵ, find the compo- nent form of V = ũ + w and sketch the specified vector…

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Q: Which of the following vectors is a unit vector orthogonal to 1 1 Select one or more: [1//3 1//3…

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Q: Let F = sin(4x +3z) i-6ye*z k. Calculate div (F) and curl (F). (Express numbers in exact form. Use…

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Q: Let B={b₁,b₂} be the basis in R2 pictured below. b₂ 0 If the coordinate vectors [11] b₁ a

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Q: Let the rotation matrices be in each of the axes 1. R. 0 cos 0 - sin 0 0 sin0 cos 0 cos 0 0 sin 0 Ry…

A: We will find out the required position of vector (7,4,1) after the rotation.

Q: Let a and b be vectors in R" such that ||a||=||||= 2 and <a,b)=3. Then ||a-b||= ..

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Q: Find the coordinate vector of a = [*]B= -10-30- 2 with respect to the basis B = for R³.

A: Given: It is given that, x→=42-4 and B=152, 01-6, 001. To find: We have to find the coordinate…

Q: Find the coordinate vector of = 48 [B = 5 -1 with respect to the basis B = 0 {} for R³.

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Q: 1. 3) Suppose A = 4i-6j, B = i + 7j and C = 9i - 5j. Find (a) ||5B-3C|| (b) unit vector having the…

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Q: Find all values of a so that u and v are orthogonal. (Enter your answers as a comma-separated list.)…

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

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

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Q: For the vectors à = (1, 0, −4) and ¯` = (5, 2, 1) what is the scalar a projection of onto a 1/17 √17…

A: The vectors are given by÷

Q: Derive the composite matrix for rotation about arbitrary point (a,b) in clockwise direction  with…

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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: Suppose v = 3i − 2j + k and b = 2i - 6j + 3k. (a) Find the vector component of v along b this is…

A: To find the vector component of vector v along vector b (proj_b(v)), you can use the projection…

Q: (7,4) by 210 4. Use matrices to rotate the vector degrees counterclockwise about the origin.

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Q: Show that the vector field A and B are everywhere perpendicular if A (2.-5,6) and B (6,5,-2)

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Q: uppose ā and b are two non-zero vectors in R3 and they are not parallel to each other. Then, their…

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Q: Consider A= (0, 4, 2), B =, (6,-1,0) and C = (3, 0, 1). 1 (a) Find the unit vector having the same…

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