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lesya [120]
4 years ago
12

Show that any three linear operators A, B, and Ĉ satisfy the following (Ja- cobi) identity (10 pt) [[A, B] Ĉ] + [[B,C), A] + [[C

, A, B) = 0
Physics
1 answer:
DerKrebs [107]4 years ago
7 0

Answer:

Three linear operators A,B, and C will satisfy the condition [[A, B],C] + [[B,C), A] + [[C, A], B] = 0.

Explanation:

According to the question we have to prove.

[[A, B],C] + [[B,C), A] + [[C, A], B] = 0

Now taking Left hand side of the equation and solve.

[[A, B],C] + [[B,C), A] + [[C, A], B]

Now use commutator property on it as,

=[A,B] C-C[A,B]+[B,C]A-A[B,C]+[C,A]B-B[C,A]\\=(AB-BA)C-C(AB-BA)+(BC-CA)A-A(BC-CB)+(CA-AC)B-B(CA-AC)\\=ABC-BAC-CAB+CBA+BCA-CAB-ABC+ACB+CAB-ACB-BCA+BAC\\=0

Therefore, it is proved that [[A, B],C] + [[B,C), A] + [[C, A], B] = 0.

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Nastasia [14]
Scientists assume the gravitational force as negligible as compared to other forces present in the an atom because its value would be very small. Gravitational force is directly proportional to the mass of an object so small mass would lead to small force as well which is true for an atom. As compared to the nuclear forces, it would have a very small value.


4 0
4 years ago
What will happen to the amount of current if a bigger battery is installed?
Hatshy [7]

Answer : Option A) Increase

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As per Ohm's law;

Voltage = Current X Resistance.

So, when a bigger battery is installed more number of electrons will flow across the circuit producing more current than before.

8 0
3 years ago
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____________ are used to calculate the distance a continent has moved in a year. a. Space satellites c. Laser beams b. Mirrors d
Law Incorporation [45]
<span> Space satellites, laser beams, mirrors</span> are used to calculate the distance a continent has moved in a year.

Therefore, your correct answer would be "all of the above".
4 0
3 years ago
An electron is moving at a speed of 4.8 × 10 6 m/s at an angle of 30.0° with respect to a uniform magnetic field of 9.2 × 10 –4
omeli [17]

Answer:

r = 5.94 10⁻² m

Explanation:

The magnetic force is given by the ratio

        F =q v x B

The bold indicate vectors and the vector product determines that the force is perpendicular to the other two vectors, so the modulus of the velocity does not change, but its direction, therefore the acceleration in Newton's second law is centripetal

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The magnitude of the force is

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The centripetal acceleration is

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Let's replace

       q v B sin θ = m v² / r

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Let's calculate

      r = 9.11 10⁻³¹  4.8 10⁶ / (1.60 10⁻¹⁹  9.2 10⁻⁴ sin 30)

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6 0
3 years ago
If the current in a wire is 2.0 amperes and the potential difference across the wire is 10.0 volts, what is the resistance of th
avanturin [10]

Answer:

v=IR

10÷2 =R

R=5 Ohm

.. .

4 0
3 years ago
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