If the vectors 2î - 3ĵ, î + ĵ - k̂ and 3î - k̂ form the three co-terminous edges of a parallelepiped, then the volume of parallelepiped is:
Step-by-step Solution:
The volume of the parallelepiped is given by the absolute value of the determinant of the matrix formed by its adjacent vectors: \[ \text{Volume} = \left| \begin{array}{ccc} 2 & -3 & 0 \\ 1 & 1 & -1 \\ 3 & 0 & -1 \end{array} \right| \] Expanding along the first row: \[ = 2 \begin{vmatrix} 1 & -1 \\ 0 & -1 \end{vmatrix} - (-3) \begin{vmatrix} 1 & -1 \\ 3 & -1 \end{vmatrix} + 0 \begin{vmatrix} 1 & 1 \\ 3 & 0 \end{vmatrix} \] \[ = 2[(1)(-1) - (0)(-1)] + 3[(1)(-1) - (3)(-1)] \] \[ = 2(-1) + 3(-1 + 3) = -2 + 3(2) = -2 + 6 = 4 \] Thus, the volume of the parallelepiped is 4.