What then is in unit-vector notation

[norcal]

1. Homework Statement

In the product F = qv x B , take q = 4,
v = 2.0i + 4.0j + 6.0k and F= 136i -176j + 72k.
What then is in unit-vector notation if Bx = By?

2. Homework Equations

136i-176j+72k = 8i+16j+24k X Bxi+Byj+Bzk

3. The Attempt at a Solution

I am stuck with the above equation. How do I solve for Bxi, Byj and Bzk?

136i-176j+72k=8i+16j+24k X Bxi+Byj+Bzk
So If I find the determinant from the right hand side it's:
136i-176j+72k=((16)(Bz)-(By)(24))i+((24)(Bx)-(Bz)(8))j+((8)(By)-(16)(Bx))k
136i-176j+72k=(16Bz-24By)i+(24Bx-8Bz)j+(8By-16Bx)k

Now what do I do?

 

[denverdoc]

1. Homework Statement

In the product F = qv x B , take q = 4,
v = 2.0i + 4.0j + 6.0k and F= 136i -176j + 72k.
What then is in unit-vector notation if Bx = By?

2. Homework Equations

136i-176j+72k = 8i+16j+24k X Bxi+Byj+Bzk

3. The Attempt at a Solution

I am stuck with the above equation. How do I solve for Bxi, Byj and Bzk?

136i-176j+72k=8i+16j+24k X Bxi+Byj+Bzk
So If I find the determinant from the right hand side it's:
136i-176j+72k=((16)(Bz)-(By)(24))i+((24)(Bx)-(Bz)(8))j+((8)(By)-(16)(Bx))k
136i-176j+72k=(16Bz-24By)i+(24Bx-8Bz)j+(8By-16Bx)k

Now what do I do?

If i were you i'd post this on one of the math forums. This isn't likely to get much response here.

 

[Andrew Mason]

1. Homework Statement

In the product F = qv x B , take q = 4,
v = 2.0i + 4.0j + 6.0k and F= 136i -176j + 72k.
What then is in unit-vector notation if Bx = By?

2. Homework Equations

136i-176j+72k = 8i+16j+24k X Bxi+Byj+Bzk

3. The Attempt at a Solution

I am stuck with the above equation. How do I solve for Bxi, Byj and Bzk?

136i-176j+72k=8i+16j+24k X Bxi+Byj+Bzk
So If I find the determinant from the right hand side it's:
136i-176j+72k=((16)(Bz)-(By)(24))i+((24)(Bx)-(Bz)(8))j+((8)(By)-(16)(Bx))k
136i-176j+72k=(16Bz-24By)i+(24Bx-8Bz)j+(8By-16Bx)k

Now what do I do?

Since i, j and k are mutually orthogonal unit vectors, then 16Bzi-24Bxi = 136i. You also know that Bx = By, so 8By-16Bx = 72 gives you the value for Bx and By. From that you can figure out Bz.

AM