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:
Explanation:
Since, entropy is the measure of degree of randomness. So, more randomly the molecules of a substance are moving more will be its entropy.
- For example, when a solid melts then it means heat is absorbed by it due to which its molecules have gained energy. As a result, they collide with each other and hence, entropy will increase.
- Evaporation of a liquid will also cause the liquid to change its state from liquid to gas. This means molecules will go far away from each other leading to an increase in the entropy.
- Sublimation is a process of conversion of a solid into gaseous phase without going through liquid phase. So, in this case also entropy will increase due to gain in energy by the molecules of a solid.
- In freezing, molecules of a substance come closer to each other and acquire less energy. Hence, entropy decreases.
- Mixing is a process of combining two or more substances physically with each other. This leads to increase in entropy of a substance.
- In separation molecules are separated from each other leading to a decrease in energy. Hence, entropy will also decrease.
- Diffusion is a process in which molecules are able to rapidly move from one place to another. Hence, entropy increases when diffusion takes place.
Thus, we can conclude that melting of a solid, evaporation of a liquid, sublimation, mixing and diffusion involve an increase in the entropy of the system under consideration.
Electrical shock is most likely to be fatal when the path of the current is through the heart.
The speed at which the objects were attracted to each other determined by the gravitational pull.
<h3>What is gravity?</h3>
The force of attraction felt by a person at the center of a planet or Earth is called as the gravity or gravitational pull.
The gravitational force, Fg is the attractive force exerted by the Earth on the object that is equal to the mass of the object times the gravitational acceleration.
When the two objects are attracted, the speed with which they are moving toward each other depends on the strength of the pull force. This pull force is the gravitational pull.
Thus, the speed at which the objects were attracted to each other determined by the gravitational pull.
Learn more about gravity.
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Plants and animals need nitrogen in order to make proteins. Proteins are essential compounds for healthy growth and fully functioning organisms.
