In the product F = qB (vectors), take q = 2 (neglecting the units of charge, q) and v = 2.0 i + 4.0 j + 6.0 k and F = 4.0 i + (-20 j) + 12 k . What then is B in unit-vector notation if Bx=By ?

Don't you mean the vector cross product

F = q V x B ?

You need to write an equation for the three components of B (with Bx = By) by rewriting the above equation for the individual components. Then solve for the Bz and Bx=By components

Had problems with the same question.

To find the B vector in unit-vector notation, we need to solve for the components Bx, By, and Bz.

Given the equation F = qB and the provided values of q and F, we can substitute them in and rearrange the equation as follows:

F = qB
4.0i + (-20j) + 12k = 2([Bx, By, Bz])

Comparing the components on both sides of the equation, we can solve for Bx, By, and Bz:

Bx = 4.0/2 = 2.0 (since q = 2)
By = -20/2 = -10.0 (since q = 2)
Bz = 12/2 = 6.0 (since q = 2)

Therefore, the B vector in unit-vector notation is B = 2.0i - 10.0j + 6.0k.