CHAPTER 1 VECTOR SCALARS AND QUESTIONS FOR DISCUSSION 1. If and are non-collinear vectors and a b ~ ~ x a 2 b  a 2 b 4 2 2 3 1       y x y and B y x x y  A ~ ~ ~ ~ 3 2 find x and y such that  A B  x 56 22 , Ans.  y 43 43 0 2. Prove that if and are non-collinear, then   implies that a b x a y b ~ ~ ~ ~ x=y=0. ~ ~ ~ ~ ~ ~ and y1=y2. 4. If , , are non-coplanar vectors determine whether the vectors a b c ~ ~ ~ ~ ~ ~ 3 5 2  a b c and 2  2 3  , r a b c r ~ ~ ~ 1 ~ ~ ~  4 5   are a b c 3 linearly independent or dependent. 5. Prove that the medians of a triangle meet in a common point that is a point of trisection of the medians. 6. Find the resultant of the following displacements: 20 km300 South of East; A, 50 km due West; 40 km Northeast; 30 km 600 South of West. B, C, D, of Ans. Magnitude 20.9 km, direction 21039ˈSouth West 7. A 100 kg mass is suspended from the center of a rope as shown in the adjoining figure. Determine the tension T in the rope. Ans. 100kg.
CHAPTER 1 VECTOR AND SCALARS QUESTIONS FOR DISCUSSION 1. If a and b are non-collinear vectors and ~ ~ A  x  4 y a  2 x  y b and B  ~ ~  y 2 x  2 a  2 x 3 y 1 b ~ ~ find x and y such that 3 A  2 B Ans. x  56 43 , y  22 43 2. Prove that if a and b are non-collinear, then x a  y b  0 implies that ~ ~ ~ ~ x=y=0. ~ ~ ~ ~ ~ ~ and y1=y2. 4. If a , b , c are non-coplanar vectors determine whether the vectors ~ ~ ~ r 1  2 a 3 b  c , r ~ ~ ~ 2  3 a 5 b  2 c and ~ ~ ~ 3  4 a 5 b  c are ~ ~ ~ linearly independent or dependent. 5. Prove that the medians of a triangle meet in a common point that is a point of trisection of the medians. 6. Find the resultant of the following displacements: A, 20 km300 South of East; B, 50 km due West; C, 40 km Northeast; D, 30 km 600 South of West. Ans. Magnitude 20.9 km, direction 21039ˈSouth of West 7. A 100 kg mass is suspended from the center of a rope as shown in the adjoining figure. Determine the tension T in the rope. Ans. 100kg.