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:
12.6 cm
Explanation:
We can use the mirror equation to find the distance of the image from the mirror:

where here we have
f = 9.50 cm is the focal length
p = 39 cm is the distance of the object from the mirror
Solving the equation for q, we find:

Answer:
Let No be initial no of atoms
N = N0 / 2 after 1 half-life
N = N0 / 4 after 2 half-lives
So after 2 half-lives 20 of the 80 atoms remain
Answer:
D
Explanation:
Gene flow is the transfer of genetic variation from one population to another
A related type of beta decay actually decreases the atomic number of the nucleus when a proton becomes a neutron. Due to charge conservation, this type of beta decay involves the release of a charged particle called a “positron” that looks and acts like an electron but has a positive charge.