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:
Given
mass of ball m=10 kg
It is placed at a height of 150 m
It is dropped from the height and allowed to free fall for 40 m
Velocity acquired by the ball during this fall is given by 
Insert u=0, a=g

Kinetic energy at this instant

To begin with, we can use the formula that links frequency, wavelength and velocity.
Because you already have the wavelength and the frequency, you just need to solve for velocity. You can do this by multiplying each side of the equation by frequency.
Therefore, 400 x 2.5 = 1000m/s.
Hope this helps :)
Answer:
Remains same
Explanation:
= Time period of oscillation
= mass
= spring constant
Time period of oscillation is given as

we know that as we move from earth to moon, the value of spring constant "k" and mass "m" remains unchanged because they do not depend on the acceleration due to gravity.
Time period depends on spring constant inversely and directly on the mass.
hence the time period remains the same.
Answer:
0.306mm
Explanation:
The radius of the conductor is 3mm, or 0.003m
The area of the conductor is:
A = π*r^2 = π*(.003)^2 = 2.8*10^-5 m^2
The current density is:
J = 130/2.8*10^-5 = 4.64*10^6 A/m
According to the listed reference:
Vd = J/(n*e) = 4.64*10^6 / ( 8.46*10^28 * 1.6*10^-19 ) = 0.34*10^-6 m/s = 0.34mm/s
The distance traveled is:
x = v*t = 0.34 * .90 = 0.306 mm