The product a (b x c) is called the scalar triple product of vectors a, b, and c. i) Using that the cross-product bxc can be calculated using a 3 x 3 matrix determinant, show that: a1 a2 a3 a (b x c) = b by bs CI C2 C3 (2 marks) The scalar triple product has a nice geometric interpretation. Consider the picture below: onilao noltup ri dang Jou auiteia anollndue The three vectors form the sides of a parallelepiped. The area of the base parallelogram is given by ||b x c, as in lectures. The height of the parallelepiped is h = We take the absolute value of cos 0 in case @ is an obtuse angle. The volume is then V = Ah = la (b x c)). Note, this is an absolute value, the dot product of two vectors is a number. This formula will give 0 if a lies in the same 2-dimensional plane as b and c. This should be clear from the diagram and how the dot-product behaves with orthogonal ||all |cos e|. %3D vectors. moltem bonunu ii) Using the scalar triple product, evaluate the volume of the parallelepiped formed by the vectors a =i+5j- 2k, b =-6i + 2j, and c = 5i+9j - 4k, explain your answer,