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3 years ago

If a=8i+j-2k and b=5i-3j+k what is the value of b X a

Physics

1 answer:

ivanzaharov [21]3 years ago

8 0

Distribute the product:

a×b = (8i + j - 2k) × (5i - 3j + k)

a×b = 8i × (5i - 3j + k) + j × (5i - 3j + k) - 2k × (5i - 3j + k)

a×b = (40 (i×i) - 24 (i×j) + 8 (i×k))

… … … + (5 (j×i) - 3 (j×j) + k×j)

… … … + (-10 (k×i) + 6 (k×j) - 2 (k×k))

Recall the definition of the cross product:

i×i = j×j = k×k = 0 (the zero vector)

i×j = k

j×k = i

k×i = j

and for any two vectors x and y, we have x×y = -(y×x).

So we have some cancellation and rewriting:

a×b = (40 (i×i) - 24 (i×j) + 8 (i×k))

… … … + (5 (j×i) - 3 (j×j) + j×k)

… … … + (-10 (k×i) + 6 (k×j) - 2 (k×k))

a×b = (-24k - 8j) + (-5k + i) + (-10j - 6i)

a×b = -5i - 18j - 29k

Then

b×a = -(a×b) = 5i + 18j + 29k

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At a constant temperature, the volume of a gas doubles when the pressure is reduced to half of its original value. This is a sta

djyliett [7]

Answer: Boyle’s law

Explanation:

Boyle's Law: This law states that pressure is inversely proportional to the volume of the gas at constant temperature and number of moles.

$P\propto \frac{1}{V}$ (At constant temperature and number of moles)

As pressure is decreased to half, the volume is increased to doubled.

Charles' Law: This law states that volume is directly proportional to the temperature of the gas at constant pressure and number of moles.

$V\propto T$ (At constant pressure and number of moles)

Gay-Lussac's Law: This law states that pressure is directly proportional to the temperature of the gas at constant volume and number of moles.

$P\propto T$ (At constant volume and number of moles)

Combined gas Law: combining the three laws:

$PV\propto T$

6 0

4 years ago

Read 2 more answers

Potential energy due to an objects compression or extension is called _______________________ energy.

cestrela7 [59]

The answer to your question is B.

8 0

4 years ago

The heating element of an iron operates at 110 V with a current of 9A. (a) What is the resistance of the iron?

Dmitrij [34]

Answer:

(A) 12.222 ohm (B) 990 W

Explanation:

We have given the voltage of the heating element V = 110 V

The current in the heating element i = 9 A

(a) According to ohm's law V =iR

So $110=9\times R$

$R=\frac{110}{9}=12.222ohm$

(b) The power dissipated in the resistor is given by $P=i^2R=9^2\times 12.222=990W$

So the power dissipated = 990 W

3 0

3 years ago

An unknown charged particle passes without deflection throughcrossed electric and magnetic fields of strengths 187,500 V/m and0.

UNO [17]

Explanation:

The given data is as follows.

Electric field strength (E) = 187,500 V/m

Magnetic field strength (B) = 0.125 T

Diameter (d) = 25.05 cm = 0.2505 m (as 1 m = 100 cm)

Radius (r) = $\frac{d}{2}$

= $\frac{0.2505}{2}$

= 0.12525 m

Formula to calculate the magnetic force ( $F_{M}$ ) is as follows.

$F_{M} = Bqv$ ............ (1)

Electrical force is calculated as follows.

$F_{E} = qE$ ............ (2)

On both electric and magnetic fields the velocity is perpendicular.

$F_{M} - F_{E}$ = 0

or, $F_{M} = F_{E}$

Hence, from equations (1) and (2)

Bqv = qE

or, v = $\frac{E}{B}$ ............. (3)

= $\frac{187500 V/m}{0.125 T}$

= 1,500,000 m/s

As the particle is moving in a semi-circular trajectory and motion of charged particle is given by the electric field as follows.

$F_{c} = \frac{mv^{2}}{r}$ ........... (4)

where, $F_{c}$ = centripetal force

$F_{M} = F_{c}$

Using equation (1) and (4) as follows.

$F_{M} = F_{c}$

Bqv = $\frac{mv^{2}}{r}$

$\frac{q}{m} = \frac{v}{Br}$

= $\frac{15 \times 10^{5}}{0.125 \times 0.12525}$

= $958.08 \times 10^{5} C/kg$

Thus, we can conclude that charge-to-mass ratio of the given particle is $958.08 \times 10^{5} C/kg$ .

8 0

3 years ago

2 diferencias y 2 similitudes entre la actividad física y el ejercicio físico.

blondinia [14]

Answer:

En el deporte, la persona que lo práctica tiene que adecuarse a él, por el contrario cuando hablamos de actividad física el objetivo pasa por programar, dosificar y adecuar en entrenamiento a las características, necesidades y objetivos de cada persona.

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3 years ago