a = i+ 2j – 2k, b 2i+ b. с ngle between a and c.

Q: V=xincペッゴ)- y bii 24 Gan prove メT5 I V, = V +2X

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Q: b) IJ 3D 10 ст, НА %3D 11 ст 55° H 25° J 140° В 60° K AK =

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Q: Write.a.ct.). in. the fa.aaT. T..aN. N. a.r(t).= (tcrst).(tsint.).j.+t.tao.

A: Here the vector r (t) = (t cos t) i + (t sin t) j + t2 k is given and write the vector in the form:…

Q: In AFGH, FG || IJ. Given that HF= 24, FG=32, and IJ 20, find HI. G HI%3D H. %3D

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Q: the g S, (x + y)e**-y*dA where R is the rectangle enclosed by x – y = 0,x – y = 2, x + y = 0, and x…

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Q: Find curl(4z i + 5xj + 9y k). curi (4z i + 5xj + 9y k) = ( i )i + ( i Ok

A: We have to find out the curl

Q: H.W. 1 Given that zl = 3 + 4i, z2 = 1 – 2i, calculate: %3D 4. 22. 21 5. zl+3 6. 2* z2

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Q: Calculate r'(t) and T(t) and evaluate T(1). r(t) = (6 + 7t,12,5 – 1²) (Give your answers using…

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Q: Let a = i − j + k, b = 3i + 5j − k, and c = −i + j + 3k. Find the indicated quantity. a · (b × c)

A: See attached file for a step by step explanation to find the required quantity.

Q: Evaluate by separation of variables. dB u(1 – u?) sec² ß | du

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Q: Find r, y, z and t where 6. + 2t 4 r+y 3 %3D -1 2 +t

A: Given  3 xyzt = x6-12t + 4x+yz+t3 We have to find x, y, z and t.

Q: » / 13t – 41º + 4 dt = 6. (а) 1 - 5 Jū du: (b) dx = 4x3 (c)

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Q: r'(t) = 12e6ti + 7ej, r(0) = 2i %3D %3D r(t) =

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Q: Hw.L showthat Vi=3inbj andVz 2-i-zj have opfosite directions.

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Q: U + 2ru, =0 IER, t> 0, u(x,0) =e=.

A: Note: As per bartleby instruction when more then one question is given only one has to be answered.…

Q: Obtain the values oF a and b Catb) + j la-b)= (itj)+j° (2+j5)

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Q: (b) Hạ: u < HO,n = 30, t = 2.431 = 0.011 P-value %3D

A: Given : Ha : u &lt; uo  n = 30  t = 2.431

Q: dp For p(q).= q¯³, dq -3 dw For w(u) = u7, du %3D %3D

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Q: dw -is equal to: dv If w = 5u, then 5w5 v(1 – 20u In v) 5w v(1 – 20w5 In v)

A: Given, w= v5w⁴ To find, dw/dv

Q: Use the equations to find az/əx and əz/ðy. e? = 8xyz %3D az 1 1 az ay %3D y

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Q: (a) Evaluate APA: – 6) R where R is the solid hemisphere r² + y² + :² – 2r + 4y = 4, : 0.

A: We want to evaluate  ∫∫∫R9-z2dV where R is the solid hemisphere x2+y2+z2-2x+4y=4, z≥0 We can write…

Q: Ex. Show that V1 = 3i + 7j & V2 =i++1)j a %3D %3D are equal ?

A: Simple vector problem...

Q: Assume Pr[A] = 0.2, Pr[B] = 0.4, and Pr[A n B] = 0.05. Fin %3D %3D %3D 1. Pr[A|B] = %3D 2. Pr[B\A] =…

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Q: H.W. 1 Given that z1 = 3 + 4i, z2 = 1 – 2i, calculate: %3D 1. z1 – 22; 2. ; 3. |21|;

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

Q: E, where 'C' i-

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Q: Determine the real number \( \alpha \) u x v and î are orthogonal, where ù = 3î + ĵ– 5k and v = 4î –…

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Q: Evaluate II, (z*y +) dz dz dy, where D = [0, 1] × [0, 1] × [1, 2]. %3D

A: Here we have to find the integration if triple integrate: ∭x2y+1zdzdxdywhere D=0,1×0,1×1,2Thus it…

Q: Calculate r'(t) and T(t), where r(t) = (2t – 5, 4 – 4t, 1 + 4t). %3D r'(t) = { %3D T(t) = {

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Q: ii. (x + y)dA Where R = {(z, y)|1 < x² + y? < 4, x < 0}

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Q: Write a in the form a = arT + aN N at t-0 for R(t) = t2i + %3D (t+r) + ( -r°*

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Q: S. Re{z²}dz; C is the square with corners 0, 1,1+i, i. [1+i]

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Q: If z=x+iy where x and y are real, find the real and imaginary parts of:- Z+1

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Q: If z = x + y, x = 2t, y = 3t, then %3D %3D 1 5 II

A: Recall:    If f(t) and g(t) are two function of 't' and h(t)=f(t)+g(t) then…

Q: Given r"(t) = , r'(0) = and r(0) = < 3, Find the j-component of r(6). %3D %3D %3D

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Q: 2. JH I TC and mJH = 40°, mJT = %3D A. 40° B. 50° C. 60° D. 70°

A: We can use the concept of arc angle in order to solve the given problem.

Q: Determine the real number \( \alpha \) u x v and î áre orthogonal, where u = 3î + ĵ – 5k and v = 4î…

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Q: Find r'(t) r(t) = e i + 8j + 3te'k r'(t) = %3D %3D

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Q: ux v of u = 2i + 3j, v = -i + j is *

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Q: d) Or I = v7 sec(0)

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Q: Find r'(t) r(t) = 6yEi + t²/ij + In[? }« %3D r'(t) = %3D

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Q: Let u = 2i−j+3k, v = 3i+j−k, and w = 3i+j+2k. Verify Equation (3).

A: Given- u=2i-j+3k,v=3i+j-k and w=3i+j+2k To verify- The equation u×v·w=u·v×w

Q: Find real numbers x, y and z such that (а) (b) 7xi + (y – 3)j + 6k = 10i + 8j – 3zk (x + 4)i + (y–…

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Q: Solve the IVP y" + 4y/ + 5y = 38,(t), y(0) = 0, y'(0) = 1. %3D %3D

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Q: solve ut = o.16 U xx %3D a sx<5O 560 U(x,o) u(o) t) = U(10,t) =0 %3D 40

A: Given PDE is ut=0.16uxx           (1) with boundary condition u(0,t)=u(100,t)=0,              (2)…

Q: 60. w %3D 5x? + 2ху — Зу?z, Р(1, 0, 1), v 3D i +j-k

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Q: Which of the following equations are true? Select three that apply. O zi - (v2) %3D (z:)'= V

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Q: Find (a) u × v, (b) v × u, and (c) v × v. u = 2i + k, v = i + 3k

A: Given that, the two vectors u = 2i + k, v = i + 3k To find the following (a) u × v, (b) v × u, and…

Q: u =-31 + 4j, v = i- 2j Jul = |2ul %3D

A: Since you have asked multiple part question, we will solve the first 3 part of the question for you…

Q: Let u = 4i + 7j and v = 7i − j. (b) Find the component of u along v. (c) Find projvu.

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Magnitude

A vector is an element with both direction and magnitude. A vector is represented using an arrow, where the arrow represents the direction of the vector and its length is represented using the magnitude. The set of vectors in space is known as vector space. The vectors can be added, subtracted, multiplied, and divided in a vector space. The image below shows a vector AB.