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:
The answer to your question is C
Because it goes from point A to point C to make one wavelenght
the answer is D, deciding what will be funded and what will be cut.
Answer: 0.798 m
Explanation:
Given
Mass of the spring oscillator, m = 1.48 kg
Force constant of the spring, k = 35.4 N/m
Speed of oscillation, v = 3.9 m/s
Kinetic Energy = 1/2 mv²
Kinetic Energy = 1/2 * 1.48 * 3.9²
KE = 0.5 * 22.5108
KE = 11.26 J
Using the law of conservation of Energy. The Potential Energy of the system is equal to Kinetic Energy of the system
KE = PE
PE = 1/2kx²
11.26 = 1/2 * 35.4 * x²
11.26 = 17.7x²
x² = 11.26 / 17.7
x² = 0.6362
x = √0.6362
x = 0.798 m
Answer:
<em>b. The current in the loop always flows in a counterclockwise direction.</em>
<em></em>
Explanation:
When a magnet falls through a loop of wire, it induces an induced current on the loop of wire. This induced current is due to the motion of the magnet through the loop, which cause a change in the flux linkage of the magnet. According to Lenz law, the induced current acts in such a way as to repel the force or action that produces it. For this magnet, the only opposition possible is to stop its fall by inducing a like pole on the wire loop to repel its motion down. An induced current that flows counterclockwise in the wire loop has a polarity that is equivalent to a north pole on a magnet, and this will try to repel the motion of the magnet through the coil. Also, when the magnet goes pass the wire loop, this induced north pole will try to attract the south end of the magnet, all in a bid to stop its motion downwards.
