Vectors a and b have magnitudes 2 and 3, respectively. If one of them is 50degrees, find the vector 5a-2b and state its magnitude.
Use the law of cosines: You know two sides, and the included angle.
Draw the figure before you compute.
I tried that but it doesn't work.
I did (5)(2^2)+(2)(3^2)-(2)(2)(3)cos50.
vector 5a has magnitude 10 and call it at 50 degrees
vector 2 b has magnitude 6 and call it at 0 degrees
so our triangle is
10 and 6 with fifty degrees between them
so the magnitude we are looking for is from
c^2 = 10^2 + 6^2 - 10*6*cos 50
that is why it did not work.
At what angle should be adjusted the two vectors to have the same value of their llA+Bll and llA-Bll?
Well, this vector seems to be having an identity crisis. Let's figure it out!
Given that the magnitude of vector a is 2 and the magnitude of vector b is 3, it seems like they're enjoying a pretty healthy lifestyle (or vector lifestyle, should I say?).
Now, one of them is at an angle of 50 degrees. But which one? That's a question only they can answer.
Let's assume vector a is the lucky one at 50 degrees. As for vector b, it remains a mystery.
Now, let's calculate the vector 5a - 2b:
5a = 5 * 2 = 10
2b = 2 * 3 = 6
So, 5a - 2b = 10 - 6 = 4
The magnitude of 5a - 2b is 4. Now it just needs to find its true direction in life!
To find the vector 5a - 2b, we need to know the direction of both vectors a and b. You mentioned that one of the vectors is 50 degrees, but we need to know which one. Let's assume that vector a is the one with a 50 degree angle.
First, let's calculate vector 5a:
- Start with vector a: magnitude of 2 and angle of 50 degrees.
- To multiply vector a by 5, we multiply the magnitude by 5: 5 * 2 = 10.
- The angle remains the same as it is just scaling the original vector.
- So, vector 5a has a magnitude of 10 and an angle of 50 degrees.
Now, let's calculate vector 2b:
- Start with vector b: magnitude of 3 and unknown angle.
- To multiply vector b by 2, we multiply the magnitude by 2: 2 * 3 = 6.
- Again, the angle remains the same.
- So, vector 2b has a magnitude of 6 and an angle that depends on the angle of vector b (which is not given).
To find the resultant vector, we subtract vector 2b from vector 5a:
- Subtracting their magnitudes: 10 - 6 = 4.
- Since we don't have the angles, we can't determine the exact angle of the resultant vector.
Therefore, the vector 5a - 2b has a magnitude of 4, but we cannot determine its exact angle without knowing the angle for vector b.