Given the two vectors u = (2, 10,5), v = (7,9,-5) (1) (a) Using the dot product as your inner product, find two vectors, x and y, that are of length one and are in the same direction of u and v respectively. (b) Find the projection of u onto v with respect to the dot product. (c) Find the distance d(u,v) with respect to the following inner product. < U, V >= U₁V₁ +2U2V2 +3U3V3.

Q: (e) Find the angle between two vectors u = (4, -3, 6) and v = (3, 0, 1).

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Q: Vector A is 35 m long and makes an angle of 60° clockwise from the positive Y-axis. Vector B is 55m…

A: We have given a vector A of magnitude 35 m and makes angle 60∘ from the positive y-axis i.e. 30∘…

Q: Find the smallest angle between the vectors v = (1,1,2) and w= (2,4,5).

A: The given vectors are,

Q: sider the following coordinates and vectors, A(-2, 1, 0), B(2, -2,0), u = 3i + 2k, v = 4i + 7j+5k,…

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Q: Locate all of the KKT points for the following problem. Con show that these points are local you…

A: Let us consider that, A=a1,a2,a3……,amn, where A∈Rm×n then there exist a constant b=b1,b2,……,bn, such…

Q: Xy - X. y X*5 lay substitution x ky algebra why 8970? a IS by algebre to? qa are botth integers and…

A: Please cheek the next step-for detailed answer

Q: Compute the resultant of the position vectors for the points (2,4,3) and (1,-5,2) of a rectangular…

A: Question- Compute the resultant of the position vectors for the points (2,4,3) and (1,-5,2) of a…

Q: (b) Find the angle between the vectors u and v if u = (2,3,5) and v = (1, -4,3) in %3D R3.

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Q: Let a = (6, −3, −5) and b = (7, -2, 10) be vectors. (A) Find the scalar projection of b onto a.…

A: Let  be vectors.(A) To find the scalar projection of .(B) To decompose the vector  into a component…

Q: Find the angle between the planes whose vector equations are 7-(2i + 2)- 36) =57-(3i -3) + Sk) = 3…

A: The solution to the the given question is explained below.

Q: Find the sine of the angle between vectors u = (-3, 2,6) and v = (3,2,6) by using the cross-product.

A: Given: The vectors u =(-3, 2, 6) and v=(3,2,6) Find : The sine of the angle between the vectors u…

Q: Consider the three vectors u = (0, -2,3), v = (1,-4,0) and w=(-4,3,-5). a) Find the cross product…

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Q: Find the cross products of vectors: u=(0,-4,2) and v=(-3,2,6). Find the area of the parallelogram…

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Q: Find the cross products u xv and vxu for the vectors u = = (3,5,0) and v = (0,3, - 6). uxv = (Di+…

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Q: 2. Consider the two vectors in R³ with components u = (2,-1,-1) and v = (-2,1+ √√3,1-√3). (a) (12…

A: Step 1: Step 2: Step 3: Step 4:

Q: 18. Find the projection of (0,4) onto (3,7).

A: Answer

Q: Determine the angles between the following pairs of vectors. (a) (−1, 1), (0, 1)     (b) (2, 0), (1,…

A: To determine the angles between the following pairs of vectors.

Q: : (2,1,2). 1- Find the unit vectors u1 and u2 in the directions of v = (1,3) and w = Find unit…

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Q: mine the angle between vectors M = (1

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Q: Sketch the vectors in the plane a= (6, 1), b=(-1, 5) Calculate the dot product a•b for the vectors…

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Q: Find the unit vectors u and uz in the directions of v = (1,3) and w = Find unit vectors U, and U2…

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Q: For the vectors u = (- 1,3) and v= (-4,2), calculate proj,u and scal,u. proj, u = D

A: Vector and scalar projection