B|a- Find u.v and v xu if u=i+2j-k and v=-2i+2j+2k

Q: a²f af af and əx' əy :f(x, y) = (x+ y)(2x + y)² Compute se дхду

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Q: Find R(t) if R′(t)=⟨1+2t,2e2t⟩ and R(0)=⟨1,3⟩.

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Q: Find V · (V × F), if F(x, y, z) = 7e**i+9xe³j – eu=k. V·(V × F) =

A: Given thatF→=7exzi+9xeyj-eyzkto find ∇.∇×F

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

A: Given vectors are (a)

Q: Solve for x, where u = (1, −1, 2), v = (0, 2, 3), and w = (0, 1, 1). 3u + 2x = w − v

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Q: df Compute if f(u) = u?, u(2) = -5, and u'(2) = -5. dx lx=2

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Q: Given F(r, s, t) =-r(8s³ +t³), compute: Frst

A: Given  Fr, s, t=-r 8s3+t3

Q: af 7. Compute and дхду a²f : f(x, y)=x'y² – sin 2 + xe" - əx' əy

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Q: 16w Given that, w =1- 2i and z = w – Calculate z.

A: w=1-2i and z=w-16 ww2

Q: If u=2i + j -3k and v=i + 4j +k, find u x v.

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Q: Q5.Given that W = f(x.y.z)% x+2y+, find : aw aw in terms of s and r, if and x=, y=r +Ins, =2rr.

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Q: Hewin If Z =R Cxxy]:and u=x-yg V=x²-y 그를 + show that

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Q: 3. Let f(x, y) = x³ 3x² + xy +7 and u = 0.6i + 0.8j, then find Duf(1,-2).

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Q: Given F(r, s, t) =r(3s² + 9t°), compute: Frst

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Q: Let v = 2i - 5j and w = -4i + 3j. Find v . w

A: We have to find the dot product value v.w for given vectors: v=2i-5j and w=-4i+3j We know that for…

Q: If ř = xî + yj + zk. Show that (i) Vř = (ii) v r3

A: Given, r→=xi^+yj^+zk^. (i) r=r→=xi+yj+zk=x2+y2+z2 Now, ∇r=∂r∂xi+∂r∂yj+∂r∂zk.…

Q: [ u#(u – 1)"-1 đu (1+x!/n dx = n

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Q: Find the values of the constants a, b, c so that F = (axy + bz3)i+ (3x² – cz)j + (3xz? – y)k Is…

A: A vector F→ is said to be irrational if and only if cure F→ =0 i.e∆ x F→ = 0Given F→ = (axy+bz3) i^…

Q: Let f(z) = kz5 + az³ + cz. Find u(x,y) if z = 3.3 + 7.8i, a = 7, c = 11, and k = 3.

A: This is a problem of complex analysis.

Q: Given u(x,t)=(1/t)e^(x^2\4t), compute: uxx

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Q: If A = *yzi – 2x² j + xz? k and B = 221 + yj – x° k, find za (AXB) at (1,0,–2). Ans. -41 - 8j

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Q: Find the value of zo so that dz = -2ri Izl=13 (z – z0) (z – 14i)

A: Given integral is ∫|z|=13z(z-z0)(z-14i)dz = -2πi   ---(1)

Q: Given F(r, s, t) = r(3s² + 3t²), compute: Frst

A: Solution of question is written in below steps.

Q: a) Find as when s = 1,t = 1 for f (x, y) = x³ – 3xy - 6x + 6y,x = 2t + s, %3D %3D y = 2s - t.

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Q: Q5: Find Zyx if Z = f(u, v) , u = xy and v = X + y. %3D

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Q: Find u · (v x w). u = 2i – 3j + 4k,v = 9i + 2j – 5k,w = 4j + 6k u · (v x w) :

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Q: If u = ₁+₂y+z, where a₁, A2, A3 al constants and J²u J²u J²u น a +a+a = 1. Show that + + = U. მ2 მყ2…

A: This question is based on Partial diffrentiation.

Q: Find u x v, v × u, and v × v. u = 6i + 8k v = 3i + 8j – 4k. (a) u x V (b) (c)

A: This question is based on cross product.

Q: solve for w where u = (0,-1,1,1) and v = (3,0,-1,2) 5w = u-3v w=?

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Q: Let u= bi + 3j and V=-2i+4; and W= 4i-3; Find wolv+ u)

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Q: Find a and b such that v au + bw, where where u (1, 2) and w - v- (0, 6)

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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: dt Determine dw if t = (6r* +3r*) -(*+2r-5)'. -s)'. and w =

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Q: Solve for w where u = = (0, 1, 1, –1) and v = (0, -1, 2, 3). %3D 5w = u - 4v W =

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Q: 1 f f(x) = : R → R, Vx2 – 4 At how many different integer points x is discontinuous? 25 - O A) 3 O…

A: We have f(x) = 1x2-4Clearly f(x) assumes real values for all real values for all x except for the…

Q: S g find Ju u and av Write the anuser in terms of U ty D Using the chain rele and V 2 to

A: Answer

Q: Q) Verify that (bx с) %3D b.(с х а) — с. (а x b) if a %34i — 3ј +6k , b- 5i +4j — 3k, с %3 4i +6j +3…

A: Given the three vectors

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: Given 7 = f (x. y)= e² , when x(u,v) = 3usin(v) and y(u,v)=8v²u, Find f„(x,y) and f,(x,y)

A: Given function is: f(x,y)=e2xyx=3usinv;  y=8v2u Substitute values of 'x' and 'y' in the given…

Q: Solve for x, where u = (1, −1, 2), v = (0, 2, 3), and w = (0, 1, 1). 3x + 2u − v + 2w = 0

A: The given vectors are Let the vector x be

Q: Find all values of x so that v · v = 1, where

A: Given vector, v=12-12x That is v=12i-12j+xk

Q: 4. and A= Find flA) where f lt) = t"-2t+3t+ 3t +2 て %3D %3D て

A: Given,  A=124-1 f(t)=t4-2t3+3t2+3t+2 Find: f(A)

Q: dw when u = 0, v = 0 if w =x? + y x= 6u - 2v + 1, y = 5u + 4v - 3. Find

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Q: Given (x)=x + 3 and v(x)=9xr - 4, find u +v O 8x +7 9x-3 Ox-4 O 10x-1 O4x + 2

A: ux=x+3and vx=9x-4We need to find u+v

Q: differentiate. a) g(t)こ3-2t St +1 c) H(u)= (u-JJ) (utro) d) FLt)- モ-3 %3D

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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: 2) find "c" s.t P(S? < c) = 0.95 if X:n(u, 12),n = 6, X2 = 11.10. %3D

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