No spacecraft has been built yet that was able to absorb harmful
radiations in space, change weather conditions on Earth, or destroy
meteors and comets which might strike Earth.
We should continue to send robotic spacecrafts into space
because they help discard some myths about objects in space.
In other words, they help us learn things that we never knew before.
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:
It is given that,
Frequency of monochromatic light,
Separation between slits,
(a) The condition for maxima is given by :
For third maxima,
(b) For second dark fringe, n = 2
Hence, this is the required solution.
The electric potential energy of the charge is equal to the potential at the location of the charge, V, times the charge, q:
The potential is given by the magnitude of the electric field, E, times the distance, d:
So we have
(1)
However, the electric field is equal to the electrical force F divided by the charge q:
Therefore (1) becomes
And if we use the data of the problem, we can calculate the electrical potential energy of the charge: