If a , b , c are mutually perpendicular vectors having magnitudes 1,2,3 respectively, then the value of [ array lll a + b + c & b - a & c array ] is

Step-by-step solution

aligned & | a |=1,| ~b |=2,| c |=3 & [ a + b + c b - a c ] & =( a + b + c ) [( b - a ) c ] & =( a + b + c ) ( b c - a c ) & =[ a b c ]-[ b a c ] & =2[ a b c ] & =2 a ( b c ) & =2| a || b c | 0^ & =2| a || b c | & =2| a || b || c | 90^ & =2 1 2 3 & =12 aligned aligned & [ array l a b and c a | b c array ] & [ b c ] aligned