In the product
`vec (F) = q (vec(v) xx vec(B)) = q vec(v) xx (B hat(i) + B hat(j) + B_0 hat(k))`
For q = 1 and ` vec(v) = 2 hat(i) + 4 hat(j) + 6 hat (k)` and `vec(F) = 4 hat(i) - 20 hat(j) + 12 hat(k)`. What will be the complete expression for `vec(B)`?

Options

A. `-6 hati - 6 hatj - 8hatk`
B. `8 hati + 8 hatj - 6hatk`
C. `6 hati + 6 hatj - 8 hatk`
D. `-8 hati - 8 hatj - 6 hatk`

Answer

A

Explanation

`F = q(vecv xx vecB)`
`vecF = vecV xx vecB " " (because q = 1)`
`4 hati - 20 hatj + 12 hatk = |{:(hati , hatj , hatk) , (2 , 4 , 6) , (B , B , B_(0)):}| = i(4B_(0) - 6B) - hatj(2B_(0) - 6B) + hatk (-2B)`
By comparison ,
`-2B = 12`
`therefore B =-6`
`4B_(0) - 6B = 4`
`4B_(0) = 6 (-6) + 4`
`4B_(0) = 4 - 36`
`B_(0) = - "" (32)/(8) = -8`
`vecB = -6hati - 6hatj - 8hatk`