Let a be a unit vector, b =2 i + j - k and c = i +3 k . Then, maximum value of [ a b c ] is

Step-by-step solution

Given that, b =2 i + j - k and c = i +3 k Now, b c = | array ccc i & j & k 2 & 1 & -1 1 & 0 & 3 array | aligned & = i (3-0)- j (6+1)+ k (0-1) & =3 i -7 j - k aligned aligned & Now, [ array lll a & b & c array ]= a ( b c ) & =| a || b c | & =1 ( 3^2+7^2+1^2 ) & = 59 & [ a b c ]_ = 59 1 & aligned ( maximum value of is 1 ) Hence, maximum value is 59 .