et x + y+ z=5 where x, y, z E R. Prove that x² + y² + z² >

Q: Calculate û x ô if û = ĵ + 2k and û = -i - ĵ + k. %3D

A: Topic = Vector   if u→ =a1i+a2j+a3k and v→ =b1i+b2j+b3kthenu→×v→=ijka1a2a3b1b2b3

Q: prove if x → y then xor y = y =

A: To prove : If x→y then x or y = y Lets use the help of truth table to prove the above statement.

Q: A fair coin is tossed two times independently. Let H₁ = {1₁ (1, if head is obtained at the ith toss…

A: When head is obtained at 1st toss then H1= 1  When head is not obtained at 1st toss then  H1= 0 When…

Q: 3) Express aw/ar and aw/as in terms of r and s if w = x +2y+z², x = 5, y = r² + Ins, z = 2r

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Q: Find div F if F(x, y, z) = (x2 + y) i + z2 j + (ey - z) k.           A . 2xy i + k          B. 2x…

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Q: Show that 1 < arg (z).

A: Inequality - A statement of an order relationship—greater than, greater than or equal to, less…

Q: for z = In(2® + y*). Find

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Q: = Evaluate S₁2₁,22,23] f (2) dz where 21 = −i, z2 = 2 + 5i, zg 5i and f(x + y) = x² + iy

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Q: Determine the length of x = 3+ (y – 2)², 4<x< 19

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Q: Q: Solve on white page clean and stepwise: Let f(x, y, z) = sinxyz, g(x, y, z) = x²yz, U = x²yi –…

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Q: Differentiate w.r.to "x" y = xsin-1x +x/(1-x3)

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Q: Find V · (V x F), if F(x, y, z) = 5e*?i+ 9xe"j – 6e²k. V · (V × F) =

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Q: aF O F2 aF, If F = F,I+Fj +F,k then prove that div F = + ду

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Q: linearise R = AT + BT

A: To linearise the below equation. R=AT+BT2

Q: (4xy) w = 3 sin (4xy tan (z) +4 In (5yz)- 8 e

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Q: Evaluate [², dx V4-x2 2.

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Q: Find those constants a, b, c, d such that f(z) = ax² + bxy + y² + i(x² + cxy + dy?)

A: The given function is : fz=ax2+bxy+y2+i(x2+cxy+dy2)

Q: Prove that 3x +8 Viv = dr dy: %3D where R [-1,1] x [0, 2).

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Q: |x? J.(V)dx = 2vIJ,(Vx) + Const. %3D

A: The Bessel function is defined as:…