Let u and v be vectors in Rn. Show that 1 1 |||u + v||² − − ||u − v||² . - 4 u. V =

Q: Find a vector v such that ||v|| = 20 and v is in the same direction as 15i + 15j

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Q: Let A and B be vectors in R. Show that ||A|| = || B|| if and only if A+ B is orthogonal to Ã- B.

A: To solve the given orthogonality problem related to vector.

Q: Suppose that u and v are vectors in Rnsuch that u•v = −1, ||u||= 2, and ||v||= 5. Find…

A: Given two vectors in u,v∈ℝn such that  u·v=-1 and u=2, v=5.   We know that for a vector a∈ℝn,…

Q: Set the vectors u and v with the points so that v.u 5-¹ ( ) = = |o||૫| 3 cos

A: To find vectors u and v that satisfy the given condition, we can start by considering the…

Q: Suppose that u and v are two vectors with |u| = 1, |v| = 4 and u · v = −2. a. Compute |u + v|. b.…

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Q: Prove that if x and y are vectors in R", then |||x|| – ||y||| < ||x- y||. X

A: Given x and y are vectors in Rn we have to prove that x−y≤x−y Since, x=x Hence,  x=x−y+yAdd and…

Q: Let u and v be vectors in R". Show that ||u – v||? – 2||u – 2v||2 + ||u – 3v||2 = 2||v||? %3D

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Q: Q2 (a) Let n E N and let ở, w e R". Show that if ở · w = 0, then || ở + w||2 = || ||² + ||w||². (b)…

A: This question can be solved using the concept of dot product of two vectors.

Q: Find a vector v such that ||v||=20 and v is in the same direction as 15i+15j.

A: The parallel vector of a vector is the scalar multiple of the vector, and if scalar is positive then…

Q: The following limit lim Select one: O None of them 8x³y³ (z,y) →(1,2) 2x - y O equals 12. O equals…

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Q: Find x∈R such that vectors a = and ?=. are equivalent

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Q: Let v = ( 1, 2 ), Find a vector w with the same direction as v such that || w || = 7.

A: Let v=1,2 Then,  v=12+22=5 The unit vector in the direction of v is, v=vv=1,25=15,25

Q: Prove that the following function is convex over the set of positive vectors: f(x1, x2, x3) =…

A: Given : A function fx1 , x2 , x3=-x1x2+2x12+2x22+3x32-2x1x2-2x2x3. To Prove that the above function…

Q: 3. Write ū as a sum of vectors, one in the direction of and another orthoganal to a. 18 [4] -5 [3³]

A: The given vector .The objective is to write the vector as a sum of vectors one in the direction of…

Q: Show that if the vectors v, w are orthogonal, then ||v + w||^2 = ||v||^2 + ||w||^2.

A: Given: The vectors v, w are orthogonal, then ||v + w||^2 = ||v||^2 + ||w||^2.

Q: Find the value of k for which the vectors 2 1 2 and -3 5 k are orthogonal. k =

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Q: |3s + 3t Let W be the set of all vectors of the form 3s - 4t. Find vectors u and v in R³ such that…

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Q: For any two vectors ū and i, ||ū + u|| = ||ū|| +||7||-

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Q: Consider the following. u = (-5, 5, 4) v = (0, 1, 6) Find u x v.

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Q: Make all obvious simplifications.

A: We have to solve

Q: Suppose |||| = 5 and |||| = 6, and assume and y are orthogonal. Then ||-||²7

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Q: Find the length of the vector v = (9, 3, 9). ||v|

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Q: = If w₁, W2, W3 are independent vectors, are the sums V₁ = W2+W3 and V₂ W₁ +W2 independent or…

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Q: If u • vx w or v • or w • v equal to zero, then the vectors u, v , and w are coplanar... True False

A: Concept Used: Three vectors are said to coplanar if their scalar triple product is zero That is  [u→…

Q: 7 Let a and b be vectors in R" such that ||a||=||b||=2 and (a,b) = 1. Then ||ab||= ...

A: Let a and b be vectors in ℝn such that  a=b=2 and &lt;a,b&gt;=72 . Then we have to find the value of…

Q: Let a = 2i and b = -2i + 3j be two-dimensional vectors. Compute la – b|.

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