If for a =2 i +3 j + k , b = i -2 j + k and c =-3 i + j +2 k , then find [a b c ] .

Step-by-step solution

The scalar triple product [ a b c ] is given by the determinant of the matrix formed by the components of the vectors a , b , and c . [ a b c ] = vmatrix 2 & 3 & 1 1 & -2 & 1 -3 & 1 & 2 vmatrix Expanding the determinant along the first row: [ a b c ] = 2((-2)(2) - (1)(1)) - 3((1)(2) - (1)(-3)) + 1((1)(1) - (-2)(-3)) [ a b c ] = 2(-4 - 1) - 3(2 + 3) + 1(1 - 6) [ a b c ] = 2(-5) - 3(5) + 1(-5) [ a b c ] = -10 - 15 - 5 [ a b c ] = -30 Answer: -30