IGNOU PHE 4 2018 - Calculate the volume of a parallelepiped whose sides are given by the

Question

Calculate the volume of a parallelepiped whose sides are given by the vectors

a = 3i +2j +k,= – i +3j and c = 2i+2j + 5k.

25 Jan 2018

Answer :

Word Count : 281

The volume of a parallelepiped formed by three vectors \(\mathbf{a}\), \(\mathbf{b}\), and \(\mathbf{c}\) is given by the absolute value of the scalar triple product: \[ V = \left| \mathbf{a} \cdot (\mathbf{b} \times \mathbf{c}) \right| \] Given vectors: \[ \mathbf{a} = 3\hat{i} + 2\hat{j} + \hat{k} \] \[ \mathbf{b} = -\hat{i} + 3\hat{j} + 0\hat{k} \] \[ \mathbf{c} = 2\hat{i}

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