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:
Add the two speeds together.
Then, divide the sum by two. This will give you the average speed for the entire trip. So, if Ben traveled 40 mph for 2 hours, then 60 mph for another 2 hours, his average speed is 50 mph.
Make the base of the building zero. Then the initial distance is 100m, final distance unknown x. Use gravity, time and initial velocity to solve for final distance.
x - 100 = (0)(5) +(1/2)(-9.81)(5^2)
x - 100 = 0 - 122.625
x = -122.625 + 100
x = -22.625 m below ground
<span>The three major types of
symbiosis are mutualism, where both species benefit, commensalism, where
one species benefits and the other is unaffected, and parasitism, where
one species benefits and the other is harmed. Symbiotic relationships can occur within an organism's body or outside of it. </span><span>Examples of mutualism include the
relationship between single-celled organisms or animals that incorporate
algae into their bodies. They give the algae necessary nutrients, and
in return receive chemical energy from the photosynthetic algae. Animals
that have this sort of relationship include some sponges, sea anemones
and clams.
Examples of commensalism include remora fish attaching to the bodies
of sharks and eating scraps of food that escape their jaws, and
barnacles living on the jaws of whales with a similar feeding strategy.
Plants have commensal relationships as well, such as many orchids that
grow on taller plants and benefit from the additional sunlight they
obtain, without actually stealing nutrients from the host plant.
Parasitic relationships are many, and parasites include all
disease-causing organisms. This category also includes insects such as
fleas that suck the blood of hosts externally. Parasitism is a very
efficient strategy for organisms, and parasites often lose many of the
features of non-parasitic life forms, instead relying on their hosts for
many of the functions of life.</span>
Answer:
A. 
B. t = 50 s
Explanation:
A. The vectorial equation of the person who is getting closer to the other person is:
r: position vector
v: speed vector = 6m/s i (if you consider the motion as a horizontal motion)
Then, you replace and obtain:
B. The time is:
d: distance to the observer = 300m
v: speed of the person on the car = 6.00 m/s
