hello!!
i'm having a little trouble converting between vector forms!!
so how would you convert the vector V = (3,40 degrees) into cartesian form
and convert v = 2i + 5j into polar form...
thanks!!
Hello, sir nerdalot!
How would you convert the vector into cartesian form
and convert into polar form?
If you sketch this diagram, the pieces should come together.We can see that: .Code:| | * | /| | r / | | / |y | / | |/θ | - - * - - + - - | x
. . . and that: .
Then use those conversion formulas . . .
Hello, sir nerdalot!
I thought about trying to use the cosine/sine rule . . . . Good thinking!
but found that there wasn't enough information to do this.
. . Well, there is . . . but it takes some Olympic-level gymnastics.
Given two vectors and , let be the angle between them.We have: .Code:Q * * \ v * \ * \ w * \ * θ \ * * * * * * * * * * O u P
. . If , then: .
Using the Law of Cosines, we have: . .[1]
A small detour:
. .
. . .[2]
Substitute [2] into [1]: .
This simplifies to: . . . . . There!