If a → , b → , c → are mutually perpendicular vectors having magnitude 1 , 2 , 3 respectively, then [ a → + b → + c → b → − a → c → ] =

Step-by-step solution

Given, | a → | = 1 ,   | b → | = 2 ,   | c → | = 3 and a → . b → = 0 = b → . c → = c → . a → (as the three vectors are mutually perpendicular) So, [ ( a → + b → + c → ) × ( b → − a → ) ] . c → = [ a → × b → − 0 + 0 − b → × a → + c → × b → - c → × a → ] . c → = [ 2 ( a → × b → ) . c → + ( c →