THE DOT CROSS PRODUCTS AND CHAPTER 2 QUESTIONS 1. If 5iˆ 2 3kˆ ; 3iˆ 2kˆ ; 3 4kˆ ; determine       A ˆj B ˆj C iˆ ˆj B  Ans. 109iˆ 7 22kˆ  ˆj   A C a) The scalar triple product A  B C b) The vector triple products i.) ii.) Ans. -12 Ans. 62iˆ 44    74kˆ ˆj A  2. Determine the value of p such that the vectors are coplanar when A, B and C 3iˆ 2 ; 4 2kˆ ;       B ˆj pkˆ C iˆ ˆj 2iˆ 4kˆ ; A    ˆj P=6 Ans. 3. Find the area of a parallelogram having diagonals 3iˆ 2kˆ 3 4kˆ .     A ˆj and B iˆ ˆj Ans. 5 3 (6,-4,4) (2,1,2) 4. Find the shortest distance from to the line joining and (3,-1,4). Ans. 3 5. A force given by is applied at the point (1,-1,2). Find the 3iˆ 2 4kˆ F   ˆj moment of about the point (2,-1,3). F Ans. 2iˆ 7 2kˆ ˆj
CHAPTER 2 THE DOT AND CROSS PRODUCTS QUESTIONS 1. If A  5iˆ 2 ˆj  3kˆ ; B  3iˆ  ˆj 2kˆ ; C  iˆ 3 ˆj  4kˆ ; determine a) The scalar triple product b) The vector triple products i.) ii.) A    A  B  C  A  B C Ans. -12 Ans. 62iˆ  44 ˆj 74kˆ Ans. 109iˆ  7 ˆj 22kˆ 2. Determine the value of p such that the vectors A, B and C are coplanar when A  2iˆ  ˆj  4kˆ ; B  3iˆ  2 ˆj  pkˆ ; C  iˆ  4 ˆj  2kˆ ; Ans. P=6 3. Find the area of a parallelogram having diagonals A  3iˆ  ˆj 2kˆ and B  iˆ 3 ˆj  4kˆ . Ans. 5 3 4. Find the shortest distance from (6,-4,4) to the line joining (2,1,2) and (3,-1,4). Ans. 3 5. A force given by F  3iˆ  2 ˆj 4kˆ is applied at the point (1,-1,2). Find the moment of F about the point (2,-1,3). Ans. 2iˆ 7 ˆj 2kˆ