(a) Consider two vectors u = 3 and v = 5 in R4, Show that 5 7 7 i) u.v = v.u ii) d(u, v) > 0 [-31

Q: The vectors u-(2,-1,1) and v= (1,1,2) in R3, the angle e between u and v is

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Q: u and i are vectors of R" such that ||ū|| = 3, |||| = 4 and the angle between them is. Determine the…

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Q: C A

A: We use Triangle law

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: Find F‘(0)  for the function f(x)=3xe5x b) Given vectors a=(1,3,-2) and b=(1,1,2) , find  3a +2b…

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Q: A chocolate factory offers 41 different types of mini chocolate treats. How many ways can a box with…

A: There are 101,270 ways to fill a box with 4 different mini chocolate treats from 41 types.3rd option…

Q: Suppose V₁, V2, V3 is an orthogonal set of vectors in R5. Let w be a vector in Span(V1, V2, V3) such…

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Q: n Let ú and ú be two nonzero vectors in R" for which ú + 2v is orthogonal to ủ – 20. What is the…

A: We have to find the ratio

Q: Consider the vectors u=(2,3,-5), V = (-3, -2,6) and w=(-4,8,4). Calculate u.v

A: We have to find u.v

Q: b Find all vectors W (W₁, W2, W3) that satisfy the equation: (3,1,4) x W = (-3,1,2).

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Q: Consider vectors u and v. Find the following. (a) u v (b) u.u u = (-3, 0, 3), v = (-1, 6, 1) (c)…

A: The given vectors are

Q: 21A)The vectors A = 3i+j+ 4k, B = 2i - 3j-k, and C = i-2j+ k, find (A x B).C

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Q: The vectors u = (-7, 1, -2) and v = (-28, x, - 8) are parallel if and only if x = - 212 %3D Select…

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Q: 10) Find two vectors of norm 1 that are orthogonal to the vectors u = and

A: Consider the provided question, u=12-23 and v=2134 Let w=ABCD be such a vector,Then, w·u=0…

Q: 7. Consider the following two vectors: u = (5, –3) and v = (2,3) (a) Evaluate |u| and |v|. (b) Find…

A: As per guidelines, we are supposed to do only the first three parts of multipart question. If you…

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: 12 2 14- = -3 are 3 Determine if the pair of vectors V₁ = 3₂ orthogonal.

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Q: Find the values of x such that the angle between the vectors and is 45°.

A: Given that The angle between the vectors 6,1,-1 and 1,x,0 is 45°.

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

A: If we have a vector u=a,b,c, then the unit vector that is in the direction of vector u is the vector…

Q: 2b.) Suppose u, w are two vectors in R' satısfyıng uXu = 4, wXw uxw = 8. What is the distance…

A: Given u and v be two vectors in ℝ7 satisfying u×u=4, w×w=16, u×w=8

Q: 3. Determine whether the vectors u and v are orthogonal, parallel or neither. (show/explain your…

A: (a). Given ,  u = 2,3,-1 and v = -1,-1,-1 (b). Given , u = j + 6k and v = i - 2j -k

Q: Show that if u and v are vectors in the three-space, then ||u x v||? = ||u|| ||||² – (u · v)²

A: u and v are vectors.

Q: 21. Given vectors u = (1,3) and v = (-6,2). a) Find u - 3v b) Find Ju + v].

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Q: What does (a b c)=0 imply with respect to the vectors: a,b,c

A: Consider the given information. The given vectors are a, b and c. Geometrically, the scalar triple…

Q: how is C equal to the difference of vectors A and B?

A: Dear user, Please read the question. We need to express Vector A in terms of sum of  B and C.

Q: Find the angle between the vectors v and w v = (−2, 3, 1)T , w = (1, 2, 4)T

A: Consider the given vectors: Here the objective is to find the angle between vector v and w.

Q: Determine the solution to the differential equation: y"(x) + y(x)y'(x) = 0, where y(0) = 0 and y'(0)…

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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