Recall the definition of the cross product with respect to the unit vectors:
i × i = j × j = k × k = 0
i × j = k
j × k = i
k × i = j
and that the product is anticommutative, so that for any two vectors u and v, we have u × v = - (v × u). (This essentially takes care of part (b).)
Now, given a = 8i + j - 2k and b = 5i - 3j + k, we have
a × b = (8i + j - 2k) × (5i - 3j + k)
a × b = 40 (i × i) + 5 (j × i) - 10 (k × i)
… … … … - 24 (i × j) - 3 (j × j) + 6 (k × j)
… … … … + 8 (i × k) + (j × k) - 2 (k × k)
a × b = - 5 (i × j) - 10 (k × i) - 24 (i × j) - 6 (j × k) - 8 (k × i) + (j × k)
a × b = - 5k - 10j - 24k - 6i - 8j + i
a × b = -5i - 18j - 29k
Answer:
45200J
Explanation:
Given parameters:
Heat of vaporization of water = 2260J/g
Mass of steam = 20g
Temperature = 100°C
Unknown:
Energy released during the condensation = ?
Solution:
This change is a phase change and there is no change in temperature
To find the amount of heat released;
H = mL
m is the mass
L is the latent heat of vaporization
Insert the parameters and solve;
H = 20g x 2260J/g
H = 45200J
Answer:
F = ⅔ F₀
Explanation:
For this exercise we use Coulomb's law
F = k q₁q₂ / r²
let's use the subscript "o" for the initial conditions
F₀ = k q² / r²
now the charge changes q₁ = q₂ = 2q and the new distance is r = 3 r
we substitute
F = k 4q² / 9 r²
F = k q² r² 4/9
F = ⅔ F₀
Answer:
The iron atom has a positive charge, making it a cation.
Explanation:
The atom has a nucleus, where the protons and neutrons, which are the subatomic particles with the highest mass, are located. Practically all the mass of the atom is concentrated in the nucleus.Protons have a positive electrical charge, while neutrons have no charge.
Electrons move around the nucleus with other negatively charged particles.
An iron atom (Fe) has 26 protons and 20 electrons in it. That is, there are 6 more protons than electrons. As mentioned, protons are positively charged. So <u><em>the iron atom has a positive charge, making it a cation</em></u>.