In the product F → = q ( v → × B → ) = q v → × B i ^ + B j ^ + B 0 k ^ For q = 1 and v → = 2 i ^ + 4 j ^ + 6 k ^ and F → = 4 i ^ - 20 j ^ + 12 k ^ What will be the complete expression for B → ?

Step-by-step solution

4 ı ^ - 20 ȷ ^ + 12 k = ( 2 ı ^ + 4 ȷ ^ + 6 k ^ ) × B ı ^ + B ȷ ^ + B o k ^ 4 ı ^ - 20 ȷ ^ + 12 k ^ = + ı ^ - ȷ ^ + k ^ 2 4 6 B B B 0 = 4 B 0 - 6 B ı ^ - 2 B 0 - 6 B ȷ ^ + ( 2 B - 4 B ) k ^ 4 B 0 - 6 B = 4 2 B 0 - 6 B = 20 2 B - 4 B = 12 ⇒ B = 6 So, 2 B 0 - 6 ( - 6 ) = 20 2 B 0 = 20 - 36 ⇒ B 0 = - 8 ∴ B → = - 6 ı ^ - 6 ȷ ^ - 8 k ^