Explain the geometrical meaning of vertor Product oftwo vectors
1 answer:
Answer:
Explained below
Explanation:
For the geometric meaning, I've attached a parallelogram showing two vectors a and B and also the angle between them as θ.
We can see that the two vectors are adjacent to each other.
So the magnitude of the product of the two vectors is simply the area of the parallelogram which is base x height. Thus;
Magnitude = |a| sin θ × |b|
This can be rewritten as;
|a|•|b| sin θ
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Recall the period of an orbit is how long it takes the satellite to make a complete orbit around the earth. Essentially, this is the same as 'time' in the distance = speed * time equation. For an orbit, we can define these quantities:
← The circumference of the orbit
speed = orbital speed, we will solve for this later
time = period
Therefore:
Where 'r' is the orbital radius of the satellite.
First, let's solve for 'v' assuming a uniform orbit using the equation:
G = Gravitational Constant (6.67 × 10⁻¹¹ Nm²/kg²)
m = mass of the earth (5.98 × 10²⁴ kg)
r = radius of orbit (1.276 × 10⁷ m)
Plug in the givens:
Now, we can solve for the period: