Let u= 31-2j + k and v= 2i – 2j + 2k. Find ux y.

Q: Find x, y e lº such that || x || ∞ = 1 = || y || = || x+y 2 || x #y.

A: As per the question we have to find two sequences x, y from the norm-space l∞ such that : ||x||∞ = 1…

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

A: It is vector problem.

Q: Q. Let a = x1 dx2 + x3 dx4, B = x1 ×2 dx3 dx4 + X3 X4 dx1 dx2 and y = x2 dx1 dx3 dx4 be forms on R4.…

A: given  α=x1dx2+x3dx4 , β=x1x2dx3dx4+x3x4dx1dx2γ=x2dx1dx3dx4 calculate  (i) αβ , αγ…

Q: Find (a) u x v, (b) v x u, and (c) v x v.

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Q: Utt = 8urr x>0 u(0, t) = 0 u(x,0) = 1 u₁(x,0) = 0

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Q: Let u=3i|-2j and v=-4i+5i find ||u||

A: Norm of a vector is given by- u2=u→.u→

Q: Find V (V x F), if F(r, y, z) = 7e""i + 2xe"j- 3e""k.

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Q: Find u x v, v x u, and v x v. u = i -j- k, v = 2i + 2j + 2k (a) u x v (b) V x u (c) V X V

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Q: Let z= I= 2e", and y = 3 ln v. Find in terms of u and v.

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Q: Find u x v, v x u, and v X V. u=i-j, v=j-k

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Q: Find all values of x and y such that Px(x,y) = 0 and P Py(x,y)=0 simultaneously. P(x,y) = 5x² -…

A: Topic = Algebra

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: 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: Use Cramer's rule to solve for y without solving for x, z, and w. 3х + y + z + = -6 W 2x + 2y z + =…

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

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Q: Find r' (2), where r(t) = u(t) × v(t), with u(2) = (1, ,2, – 1), u' (2) = (3, ,0, 4) , and v(t) =…

A: Solution :-

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: 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: If u = x²zî + yz?j – xyk and 0 = x²yz then find the value of u. (To)

A: Consider a function fx,y,z. The gradient of the function can be defined as, ∇→f=∂f∂xi^+∂f∂yj^+∂f∂zk^…

Q: Find V. (F x G), if F(x, y, z) = 8xi+j+7yk and G(x, y, 2) = xi + yj – zk. V: (F x G)

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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: 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: Find r(t) u(t). 1 r(t) =D (5t-7)i + 하 + 2k %3D u(t) = t²i – 4j + Pk %3D r(t) · u(t) = %3D

A: Vector Question

Q: Given u = 4i - 3j and v = -6i + 4j, calculate u· v.

A: See the attachment

Q: Find V · (F × G), if F(x, y, z) = 2xi+j+14yk and G(x, y, z) = xi+ yj – zk. %3D - V · (F × G) = %3D

A: Given: F→x,y,x=2xi^+j^+14yk^ and G→x,y,x=xi^+yj^-zk^. To evaluate: ∇·F→×G→

Q: Find V· (F x G), if F(x, y, z) = 11xi+j+ 4yk and G(x, y, z) = xi+ yj – zk. V· (F × G)

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

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Q: If u = ex+₂y+azz, Show that d² u əx² + where a₁, a2, as are constants and a² + a² + a² = 1. J² u 8²…

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Q: Find V · (V × F), if F(x, y, z) = 6e²*i+ 5xe"j – 2ev³k. %3D -

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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: Find V (F x G), if F(x, y, z) = 11xi +j+ 13yk and G(x, y, z) = xi + yj – zk. V. (F x G) =

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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: Let u=2i+3j-2k and v=-1i-4j +k Find u . v, ||u|| and u . v

A: Given that u and v vector and we find its dot product (u.v) and mode of u(||u||). Here i attached…

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

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Q: Let F(x, y) = xy + 2y² + 20x + 6y + 33. Find all values of y such that F(y, y) = –2.

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

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Q: Find V· (F x G), if F(x, y, z) = 10xi +j+7yk and G(x, y, z) = xi+ yj – zk. V · (F × G) =

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Q: Find r(t) u(t). r(t) = (5t – 4)i +j - +2k 2. %3D u(E) = i - 4j - ēk %3D | r(t) u(t) -

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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: If f(x,y,z)=exp(3x)cos(-4yz), find Vf. %3D

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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: Find V· (F x G), if F(x, y, z) = 6xi+j+15yk and G(x, y, z) = xi + yj – zk. V · (F × G) =

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Q: Let f (z) =iz - 7x. Which of the following is correct ? oi4 = - 7 v, и 3D — olu =7 v oi4 = - 7 v,…

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Q: Let z = f(x, y) = In(x² + y²), when x = 2, y = 3, and dx = 1, dy = 0.5, then %3D %3D %3D dz = Select…

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Q: Find V (F x G), if F(r, y, z) G(x, y, z) = xi+ yj - zk. = 2xi +j+ 8yk and V. (F x G) =

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Q: Eliminate the parameter t: x = (v0cosa)t, y = (v0sina)t-16t2

A: *to find:- equation in the form of x & y only, by eliminating the parameter t.

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

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