What then is in unit-vector notation if Bx = By?

[norcal]

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?

Homework Equations

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

The Attempt at a Solution

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

 

[GmL]

You're not adding the B-components, you're taking the cross product. Recall the 3x3 matrix with i, j, and k in r1. You have to find the determinant of that matrix to solve for F, which is given to you.

 

[norcal]

oops I did a typo. I know that. It's:
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?