Answer:
a) (0, -33, 12)
b) area of the triangle : 17.55 units of area
Explanation:
<h2>
a) </h2>
We know that the cross product of linearly independent vectors 
and 
gives us a nonzero, orthogonal to both, vector. So, if we can find two linearly independent vectors on the plane through the points P, Q, and R, we can use the cross product to obtain the answer to point a.
Luckily for us, we know that vectors 
and 
are living in the plane through the points P, Q, and R, and are linearly independent.
We know that they are linearly independent, cause to have one, and only one, plane through points P Q and R, this points must be linearly independent (as the dimension of a plane subspace is 3).
If they weren't linearly independent, we will obtain vector zero as the result of the cross product.
So, for our problem:
<h2>B)</h2>
We know that and are two sides of the triangle, and we also know that we can use the magnitude of the cross product to find the area of the triangle:
so:
Answer:
Explanation:
The speed increased from 2.0 * 10^7 m/s to 4.0 * 10^7 m/s over a 1.2 cm distance.
Let us find the acceleration:
Electric force is given as the product of charge and electric field strength:
F = qE
where q = electric charge
E = Electric field strength
Force is generally given as:
F = ma
where m = mass
a = acceleration
Equating both:
ma = qE
E = ma / q
For an electron:
m = 9.11 × 10^{-31} kg
q = 1.602 × 10^{-19} C
Therefore, the electric field strength of the electron is:
Answer:
C.Vacuum
Explanation:
There are three methods of transfer of heat:
1) Conduction: conduction is the transfer of heat by direct contact between the molecules of two objects (or two substances). The particles of the hotter object vibrate faster than the particles of the colder object, so energy is transferred by collisions of the molecules from the hotter object to the colder object.
2) Convection: convection is the transfer of heat by mass movement of molecules. This occurs in fluids (liquids or gases), when an external source of heat is applied to the fluid. As a result, the part of the fluid closer to the source gets warmer, so it becomes less dense and rises, while the colder part sinks and replaces the hotter part, forming a convective current. The process continues until the heat source is removed.
3) Radiation: radiation is the transfer of heat carried by electromagnetic waves. Electromagnetic waves can travel in any medium and in a vacuum, so they are the only type of heat transfer that can occur in a vacuum (while conduction and convection cannot occur in a vacuum).
Answer:
The back end of the vessel will pass the pier at 4.83 m/s
Explanation:
This is purely a kinetics question (assuming we're ignoring drag and other forces) so the weight of the boat doesn't matter. We're given:
Δd = 315.5 m
vi = 2.10 m/s
a = 0.03 m/s^2
vf = ?
The kinetics equation that incorporates all these variables is:
vf^2 = vi^2 + 2aΔd
vf = √(2.1^2 + 2(0.03)(315.5))
vf = 4.83 m/s
