Find the indicated quantity, assuming that u = 7i + j, v = i − 3j, and w = 3i + 5j. u · (v + w)

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A: Answer(1): Given that, w = f(x, y)  and  x = r cos θ, y = r sin θ Now, to find formulas for ∂w∂r,…

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Q: Find the indicated quantity, assuming that u = 5i + j, v =i - 3j, and w 3i + 7j. %3D %3D u (v + w)

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Q: Find the indicated quantity, assuming that u = 7i + j, v = i − 3j, and w = 3i+2j.     u · (v + w)

A: Compute v+w as follows.

Q: Find the indicated quantity, assuming that u = 5i + j, v = i – 3j, and w = 3i + 6j. u (v + w)

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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.

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A: Given v=3i+j+3k, w=i-k

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A: Given: a=i-j+k, b=4i+5j-k, c=-i+j+4k To evaluate: a·b×c Cross product of two vectors r→=ai^ +…

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A: Using the substitutions we will solve for the PDE given as follows: ∂u∂x+y∂u∂y=x ∂u∂x+y∂u∂y=x…

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A: Here the solution of the given partial differential equation is given in terms of unknown function.…

Q: Find the indicated quantity, assuming u = 7i + j, v = i - 3j, and w = 3i + 5j. (u + v) · (u – v)

A: Givenu=7i+jv=i-3ju+v=7i+j+i-3j=8i-2ju-v=7i+j-(i-3j)=7i+j-i+3j=6i+4j

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Q: Calculate the given quantity if u = i +j- 4k v = 5i – 2j + k w = j- 3k. (a) 2u + 3v (b) |u| (c) u v

A: For solution see step 2.

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A: We have given: at=8cost kv0=4i+6jr0=7i We know that at=dvtdt So, we can write this as: dvt=at…

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A: Since you have asked multiple Sub- parts,as per our company guidelines we are supposed to answer…

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A: x(i+j+k)+y(i-j+2k)+z(i+k)=2i+k  =&gt;(x+y+z)i+(x-y)j+(x+2y+z)k = 2i+k Now, comparing the…

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A: Given that  To find the partial derivative of w with respect to u

Q: Find the indicated quantity, assuming that u = 2i + j, v = i − 3j, and w = 3i + 7j. u · (v + w)

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A: We have to find partial derivative.

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Q: 8. Calculate the given quantity if u = i+j- 2k v = 31 - 2j + k w = j- 5k (а) 2u + 3v (b) |u| (c) u-v…

A: Hello, thanks for the question. Since we only answer up to 3 sub-parts, we’ll answer the first 3.…

Q: Find the indicated quantity, assuming u = 6i + j, v = i - 3j, and w = 3i + 7j. (u + v) · (u – v)

A: We know,  i·i=1 ; i·j=0 ; i·k=0j.i=0 ; j·j=1 ; j·k=0k.i=0 ; k·j=0 ; k·k=1

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A: The vector is A→=1x2+y2xyz-3xy ax+zy2+3x2 ay+xy az At P1, 2, 4, A→=152 ax+19 ay+2 az We know,…

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A: Hey, since there are multiple subparts posted, we will answer the first question. If you want any…

Q: Calculate the given quantity if u =i+j- 4k v = 5i - 2j + k w j- 3k. (a) 2u + 3v (b) Ju| (c) u. V (d)…

A: u=11-4,  v=5-21,  w=01-3 . 2u+3v=211-4+35-21 2u+3v=22-8+15-63 2u+3v=17-4-5 2u+3v=17i-4j-5k

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Q: (b) Determine whether u(x,t)= e' sinx is a solution to L

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Q: Find the indicated quantity, assuming that u = 4i + j, v = i − 3j, and w = 3i + 2j. u · v + u · w

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Q: The coefficient of r cos e in the general solution of U,+u,+u90 =0; 1<r<2,

A: In this question, we have given Laplace equation in polar form. Here we use the general solution of…

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

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

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Q: Find Vf at the given point. f(x,y,z) = ex+Y sin z+ (y + 1) cos "x, Vf i+ 0,0, (Type an exact answer,…

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Q: Evaluate by using homogeneous D.E. 3 (3x? + y) dx – 2xydy = 0 03 In(x2 + y?) + 4 = C O a = C(9x³ +…

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Q: (b) Oppositely directed to 18i – 12j + 6k. - 3 i 1 j + k V6

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Q: Given w= (x+ y+z) , x=r-s, y=cos(r +s) , and z = sin(r +s) , %3|

A: Given  w=x+y+z2x=r−sy=cos(r+s)z=sin(r+s)

Q: Find ∫C  ez / (z - πi) dz where C is defined as z(t) = 4eit and 0 ≤ t ≤ 2π.

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Q: Find r(t) if r'(t) = 7tºi + 10t°j + VEk and r(1) = i+ j. %3D

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Q: (c) u V (d) u x v -7i – 21j – 7k (e) |v x w| V 275 (f) u (v x w) the angle between u and v (rounded…

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Q: Find V · (V × F), if F(x, y, z) = e2²i+ 7xe'j – 2e²k. - V·(V × F) =

A: Solved below

Q: 8. Calculate the given quantity if u = i+j- 2k v = 31 - 2j + k w = j- 5k (а) 2и + 3v (b) |u| (c) u-v…

A: Given vectors - u = i+j-2kv = 3i-2j+kw = j-5kPart (a) - 2u+3v = 2i+j-2k+33i-2j+k2u+3v =…

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Q: show that J (x) 2 sin X %3D (-Um ,?m + Salt- Je Cx) = zm+ (m!)P (m++1) M=D0

A: Given