How to calculate special vector notation?












0















I have some problems verifying an already calculated bill in javascript.
I gave some formulas and 2 vectors - but no matter how I calculate, I don't get the right result.



I would be happy if someone could discover my careless mistake and help me, because at the moment I am really helpless.





  1. These vector are given:



    enter image description here



  2. These are the formulas for calculating the two angles angles (alpha and beta):



img1




  1. This is the basic formula for calculation the vectors scale:
    formula1


Here you can find the result of the calculation (I'm not getting the same result):



omg3




This is my javascript code:






let u = [1, -0.2]

let v = [0.5, 0.8]



let mg_u = Math.sqrt(u[0] ** 2 + u[1] ** 2)

let mg_v = Math.sqrt(v[0] ** 2 + v[1] ** 2)

let sc_uv = u[0] * v[0] + u[1] * v[1]



let a = Math.sqrt((mg_v ** 2 - mg_u ** 2 + Math.sqrt((mg_v ** 2 - mg_u ** 2) ** 2 + 4 * (sc_uv ** 2))) / 2)

let b = (-sc_uv) / a

console.log(`alpha: ${a} (valid)`)

console.log(`beta: ${b} (valid)`)



let u_r = [-u[1], u[0]]

let v_r = [-v[1], v[0]]



let scale = Math.sqrt(mg_u ** 2 + a ** 2) /

  Math.sqrt(Math.sqrt((v_r[0] - b * u_r[0]) ** 2 + (v_r[1] - b * u_r[1]) ** 2) ** 2 + mg_u ** 2 + mg_v ** 2)

console.log(`scale: ${scale} (probably not valid)`)



let direction = [

  v_r[0] - b * u_r[0],

  v_r[1] - b * u_r[1],

]

console.log(`direction: ${direction} (not valid)`)








javascript math vector calculation







share|improve this question























  • I had a quick go at calculating the 'so that' using the values supplied in the example and I don't get the same answer, but I could be doing it wrong... is the example you are using wrong?

    – Matthew Page
    Jan 20 at 11:02











  • I'm pretty sure the example and it's value are correct. But if we both have the same mistake maybe it is. This would explain a lot.

    – jonas00
    Jan 20 at 11:04











  • The given final result is indeed incorrect, or at least inconsistent with the other values. The ratio of the components of v_r - b * u_r is -0.5822... from the given intermediate values, but -0.4904... from the result.

    – meowgoesthedog
    Jan 21 at 10:44
















0















I have some problems verifying an already calculated bill in javascript.
I gave some formulas and 2 vectors - but no matter how I calculate, I don't get the right result.



I would be happy if someone could discover my careless mistake and help me, because at the moment I am really helpless.





  1. These vector are given:



    enter image description here



  2. These are the formulas for calculating the two angles angles (alpha and beta):



img1




  1. This is the basic formula for calculation the vectors scale:
    formula1


Here you can find the result of the calculation (I'm not getting the same result):



omg3




This is my javascript code:






let u = [1, -0.2]

let v = [0.5, 0.8]



let mg_u = Math.sqrt(u[0] ** 2 + u[1] ** 2)

let mg_v = Math.sqrt(v[0] ** 2 + v[1] ** 2)

let sc_uv = u[0] * v[0] + u[1] * v[1]



let a = Math.sqrt((mg_v ** 2 - mg_u ** 2 + Math.sqrt((mg_v ** 2 - mg_u ** 2) ** 2 + 4 * (sc_uv ** 2))) / 2)

let b = (-sc_uv) / a

console.log(`alpha: ${a} (valid)`)

console.log(`beta: ${b} (valid)`)



let u_r = [-u[1], u[0]]

let v_r = [-v[1], v[0]]



let scale = Math.sqrt(mg_u ** 2 + a ** 2) /

  Math.sqrt(Math.sqrt((v_r[0] - b * u_r[0]) ** 2 + (v_r[1] - b * u_r[1]) ** 2) ** 2 + mg_u ** 2 + mg_v ** 2)

console.log(`scale: ${scale} (probably not valid)`)



let direction = [

  v_r[0] - b * u_r[0],

  v_r[1] - b * u_r[1],

]

console.log(`direction: ${direction} (not valid)`)








javascript math vector calculation







share|improve this question























  • I had a quick go at calculating the 'so that' using the values supplied in the example and I don't get the same answer, but I could be doing it wrong... is the example you are using wrong?

    – Matthew Page
    Jan 20 at 11:02











  • I'm pretty sure the example and it's value are correct. But if we both have the same mistake maybe it is. This would explain a lot.

    – jonas00
    Jan 20 at 11:04











  • The given final result is indeed incorrect, or at least inconsistent with the other values. The ratio of the components of v_r - b * u_r is -0.5822... from the given intermediate values, but -0.4904... from the result.

    – meowgoesthedog
    Jan 21 at 10:44














0












0








0


1






I have some problems verifying an already calculated bill in javascript.
I gave some formulas and 2 vectors - but no matter how I calculate, I don't get the right result.



I would be happy if someone could discover my careless mistake and help me, because at the moment I am really helpless.





  1. These vector are given:



    enter image description here



  2. These are the formulas for calculating the two angles angles (alpha and beta):



img1




  1. This is the basic formula for calculation the vectors scale:
    formula1


Here you can find the result of the calculation (I'm not getting the same result):



omg3




This is my javascript code:






let u = [1, -0.2]

let v = [0.5, 0.8]



let mg_u = Math.sqrt(u[0] ** 2 + u[1] ** 2)

let mg_v = Math.sqrt(v[0] ** 2 + v[1] ** 2)

let sc_uv = u[0] * v[0] + u[1] * v[1]



let a = Math.sqrt((mg_v ** 2 - mg_u ** 2 + Math.sqrt((mg_v ** 2 - mg_u ** 2) ** 2 + 4 * (sc_uv ** 2))) / 2)

let b = (-sc_uv) / a

console.log(`alpha: ${a} (valid)`)

console.log(`beta: ${b} (valid)`)



let u_r = [-u[1], u[0]]

let v_r = [-v[1], v[0]]



let scale = Math.sqrt(mg_u ** 2 + a ** 2) /

  Math.sqrt(Math.sqrt((v_r[0] - b * u_r[0]) ** 2 + (v_r[1] - b * u_r[1]) ** 2) ** 2 + mg_u ** 2 + mg_v ** 2)

console.log(`scale: ${scale} (probably not valid)`)



let direction = [

  v_r[0] - b * u_r[0],

  v_r[1] - b * u_r[1],

]

console.log(`direction: ${direction} (not valid)`)








javascript math vector calculation







share|improve this question














I have some problems verifying an already calculated bill in javascript.
I gave some formulas and 2 vectors - but no matter how I calculate, I don't get the right result.



I would be happy if someone could discover my careless mistake and help me, because at the moment I am really helpless.





  1. These vector are given:



    enter image description here



  2. These are the formulas for calculating the two angles angles (alpha and beta):



img1




  1. This is the basic formula for calculation the vectors scale:
    formula1


Here you can find the result of the calculation (I'm not getting the same result):



omg3




This is my javascript code:






let u = [1, -0.2]

let v = [0.5, 0.8]



let mg_u = Math.sqrt(u[0] ** 2 + u[1] ** 2)

let mg_v = Math.sqrt(v[0] ** 2 + v[1] ** 2)

let sc_uv = u[0] * v[0] + u[1] * v[1]



let a = Math.sqrt((mg_v ** 2 - mg_u ** 2 + Math.sqrt((mg_v ** 2 - mg_u ** 2) ** 2 + 4 * (sc_uv ** 2))) / 2)

let b = (-sc_uv) / a

console.log(`alpha: ${a} (valid)`)

console.log(`beta: ${b} (valid)`)



let u_r = [-u[1], u[0]]

let v_r = [-v[1], v[0]]



let scale = Math.sqrt(mg_u ** 2 + a ** 2) /

  Math.sqrt(Math.sqrt((v_r[0] - b * u_r[0]) ** 2 + (v_r[1] - b * u_r[1]) ** 2) ** 2 + mg_u ** 2 + mg_v ** 2)

console.log(`scale: ${scale} (probably not valid)`)



let direction = [

  v_r[0] - b * u_r[0],

  v_r[1] - b * u_r[1],

]

console.log(`direction: ${direction} (not valid)`)








let u = [1, -0.2]

let v = [0.5, 0.8]



let mg_u = Math.sqrt(u[0] ** 2 + u[1] ** 2)

let mg_v = Math.sqrt(v[0] ** 2 + v[1] ** 2)

let sc_uv = u[0] * v[0] + u[1] * v[1]



let a = Math.sqrt((mg_v ** 2 - mg_u ** 2 + Math.sqrt((mg_v ** 2 - mg_u ** 2) ** 2 + 4 * (sc_uv ** 2))) / 2)

let b = (-sc_uv) / a

console.log(`alpha: ${a} (valid)`)

console.log(`beta: ${b} (valid)`)



let u_r = [-u[1], u[0]]

let v_r = [-v[1], v[0]]



let scale = Math.sqrt(mg_u ** 2 + a ** 2) /

  Math.sqrt(Math.sqrt((v_r[0] - b * u_r[0]) ** 2 + (v_r[1] - b * u_r[1]) ** 2) ** 2 + mg_u ** 2 + mg_v ** 2)

console.log(`scale: ${scale} (probably not valid)`)



let direction = [

  v_r[0] - b * u_r[0],

  v_r[1] - b * u_r[1],

]

console.log(`direction: ${direction} (not valid)`)





let u = [1, -0.2]

let v = [0.5, 0.8]



let mg_u = Math.sqrt(u[0] ** 2 + u[1] ** 2)

let mg_v = Math.sqrt(v[0] ** 2 + v[1] ** 2)

let sc_uv = u[0] * v[0] + u[1] * v[1]



let a = Math.sqrt((mg_v ** 2 - mg_u ** 2 + Math.sqrt((mg_v ** 2 - mg_u ** 2) ** 2 + 4 * (sc_uv ** 2))) / 2)

let b = (-sc_uv) / a

console.log(`alpha: ${a} (valid)`)

console.log(`beta: ${b} (valid)`)



let u_r = [-u[1], u[0]]

let v_r = [-v[1], v[0]]



let scale = Math.sqrt(mg_u ** 2 + a ** 2) /

  Math.sqrt(Math.sqrt((v_r[0] - b * u_r[0]) ** 2 + (v_r[1] - b * u_r[1]) ** 2) ** 2 + mg_u ** 2 + mg_v ** 2)

console.log(`scale: ${scale} (probably not valid)`)



let direction = [

  v_r[0] - b * u_r[0],

  v_r[1] - b * u_r[1],

]

console.log(`direction: ${direction} (not valid)`)





javascript math vector calculation




javascript math vector calculation






share|improve this question













share|improve this question











share|improve this question




share|improve this question










asked Jan 20 at 10:29









jonas00jonas00

8921620




8921620













  • I had a quick go at calculating the 'so that' using the values supplied in the example and I don't get the same answer, but I could be doing it wrong... is the example you are using wrong?

    – Matthew Page
    Jan 20 at 11:02











  • I'm pretty sure the example and it's value are correct. But if we both have the same mistake maybe it is. This would explain a lot.

    – jonas00
    Jan 20 at 11:04











  • The given final result is indeed incorrect, or at least inconsistent with the other values. The ratio of the components of v_r - b * u_r is -0.5822... from the given intermediate values, but -0.4904... from the result.

    – meowgoesthedog
    Jan 21 at 10:44



















  • I had a quick go at calculating the 'so that' using the values supplied in the example and I don't get the same answer, but I could be doing it wrong... is the example you are using wrong?

    – Matthew Page
    Jan 20 at 11:02











  • I'm pretty sure the example and it's value are correct. But if we both have the same mistake maybe it is. This would explain a lot.

    – jonas00
    Jan 20 at 11:04











  • The given final result is indeed incorrect, or at least inconsistent with the other values. The ratio of the components of v_r - b * u_r is -0.5822... from the given intermediate values, but -0.4904... from the result.

    – meowgoesthedog
    Jan 21 at 10:44

















I had a quick go at calculating the 'so that' using the values supplied in the example and I don't get the same answer, but I could be doing it wrong... is the example you are using wrong?

– Matthew Page
Jan 20 at 11:02





I had a quick go at calculating the 'so that' using the values supplied in the example and I don't get the same answer, but I could be doing it wrong... is the example you are using wrong?

– Matthew Page
Jan 20 at 11:02













I'm pretty sure the example and it's value are correct. But if we both have the same mistake maybe it is. This would explain a lot.

– jonas00
Jan 20 at 11:04





I'm pretty sure the example and it's value are correct. But if we both have the same mistake maybe it is. This would explain a lot.

– jonas00
Jan 20 at 11:04













The given final result is indeed incorrect, or at least inconsistent with the other values. The ratio of the components of v_r - b * u_r is -0.5822... from the given intermediate values, but -0.4904... from the result.

– meowgoesthedog
Jan 21 at 10:44





The given final result is indeed incorrect, or at least inconsistent with the other values. The ratio of the components of v_r - b * u_r is -0.5822... from the given intermediate values, but -0.4904... from the result.

– meowgoesthedog
Jan 21 at 10:44












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