A Problem. If A and B are vectors in R" and B + 0, let P = ProjR A and show that ||| ||A-P|| |||° = |P||? + || A – P||? ||P|| P=Proj, B

Q: 81. Given r = (-3, 4) and s = a. Find the product ||r|||s||. (9. – 12). b. Find r· s. c. Based on…

A: Given:r=-3,4 and s=9,-12Formula:u=u.u

Q: a. (a+ (а x b)) Choose... (a x b) + (b x a) Choose... аx (а.b) Choose... а. (а х b) Choose...

A: It is vector calculation

Q: and ā is a cC 7) will be

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Q: If u and are the vectors below, find the vector w whose tail is at the point halfway from the tip of…

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Q: Let A = (4, –4,4, 0) and B = (-4,3, –4, 1) be points in R*

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

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: The vectors p and q span R2 For which values of k will (k2 + 2k - 3)p + (k2 +k - 6)q = 0 Explain…

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Q: Consider the array of vectors in the figure below. +y G H. R K A L 1. A + B + C + D + Q + H + Í + J…

A: # We are entitled to solve one question at a time, please resubmit the other question if you wish to…

Q: Suppose that u and v are vectors in R7 both of length 2√2 and that the length of u - v is also²√².…

A: Solution :

Q: 7. Let -4 4 a. How many vectors are in {V1, V2, V3}? b. How many vectors are in Col A? c. Is p in…

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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: If some p vectors can span V, then dim V= p True False

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Q: Suppose that u, v, and w are vectors such that = 3, = -2, = 5, llull Evaluate the following…

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Q: 6. Prove that A ·B+ |A x B|< 2|A||B|| for arbitrary vectors A, B and C.

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

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Q: 11. Find the rate.cf.changf.f.at.P.in.the directod then.vectoe ūf a. f.=ylnx. P(1,-3. --3 P.(I,-3..…

A: Directional derivative

Q: Which of the following statements are true for all vectors a, b? A. ||a - - b||² B. a∙b=0⇒a=0 C. a.…

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Q: A v xu u = (1,3,-3), v = (4,0.2) T......

A: Let's find.

Q: Suppose u, v are vectors in V. Then ||u – 2v|| = Select one: O a. ||u|| + ||v||' +2Re O b. ||u|| +…

A: Consider u and v are two vectors in V. The objective of the problem is to find the value of…

Q: 2. a. In each part express the vector as a linear combination of 2+x+4x², p₂ = 1 − x + 3x², and p3 =…

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Q: Let vi = 2 v2 , V3 = -3 3 Does the set of vectors {v, ,v2, v3} span R3 ? Give reason(s) for your…

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Q: The number of named Atlantic storms for 9 consecutive years is: 7, 8, 14, 11, 12, 7, 6, 11, 13., We…

A: As per our guidelines we can solve first three sub part of question and rest can be reposted.…

Q: For any two vectors ā and 5, show that (1+laf)(1+|5)=|1-a5f +a+5+āxbf.

A: Explained below

Q: If the vectors in the figure satisfy |u| = |v| = 1 and u+v+ w = 0, what is ❘w|? |W| = u W

A: The problem is asking for the magnitude of vector w given that the magnitudes of vectors u and v are…

Q: u = [-5, –1] v = [9, –7) w = [8, 1] 5u + v – w = [ Ex: 6

A: We will use the co-ordinate wise vector addition definition in R² where, u, v, w are vectors in the…

Q: - ()--)- 1 Let a = 2 and b = be two vectors. What is Jal2|b|2 - |a · bl2 ?

A: Here,  Given that  two vectors  . So, we find the value of  |a|^2.|b|^ - |a.b|^2

Q: ind the values of h for which the set of vectors (13] 778 linearly independent. Do not use a…

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