The volume of the parallelopiped whose coterminous edges are 2 i + j - k , 3 i - j - k , j + 3 k is

Step-by-step solution

Let the coterminous edges be a = 2 i + j - k , b = 3 i - j - k , and c = j + 3 k . The volume of the parallelopiped is given by the absolute value of the scalar triple product [ a b c ] . [ a b c ] = vmatrix 2 & 1 & -1 3 & -1 & -1 0 & 1 & 3 vmatrix Expanding the determinant along the first row: [ a b c ] = 2(-3 + 1) - 1(9 - 0) - 1(3 - 0) [ a b c ] = -4 - 9 - 3 = -16 V = |-16| = 16 cu. units. Answer: 16 cu. units