CHAPTER 2 THE DOT CROSS PRODUCTS AND Example 2.15 If  2iˆ 3  4kˆ ,  2 3kˆ  2iˆ   2kˆ . A B iˆ and C ˆj ˆj ˆj iˆ kˆ ˆj 1 2 3 Then B  C  2 1 2 8 5kˆ   ˆj  8  5kˆ ˆj     A 8  5k ˆ ˆ   24  20  42 Scalar triple products satisfy the following properties: A A A B A C A A B 3 (i) A C C 1 B B B B B A C A 1 2 3 1 B Since interchanging two rows in a determinant reverses the sign.       Then A B since two rows are identical 1 3 A A A (ii) A A A The scalar triple product in absolute represents the volume of a parallelepiped with sides . , A B and C COPLANAR VECTORS The scalar triple product provides a test to show whether three given vectors lie in the same plane. A BC
CHAPTER 2 THE DOT AND CROSS PRODUCTS Example 2.15 If A  2iˆ 3 ˆj  4kˆ , B  iˆ 2 ˆj 3kˆ and C  2iˆ  ˆj  2kˆ . iˆ ˆj kˆ Then B  C  1 2 3 2 1 2  8 ˆj  5kˆ  8 ˆj  5kˆ A    ˆ 8 ˆ  5k    24  20  42 Scalar triple products satisfy the following properties: (i) B B B A 1 2 3 1 A A A B A C B A A 3 1 B C A B C A B C Since interchanging two rows in a determinant reverses the sign. Then A       (ii) A 1 A A B A A 3 A since two rows are identical The scalar triple product in absolute represents the volume of a parallelepiped with sides A , B and C . COPLANAR VECTORS The scalar triple product provides a test to show whether three given vectors lie in the same plane. A BC