## N – 2.2 – Product of two vectors – Exercise Problems with solutions

Soln: = 1(1) + 1(1) + 0 = 1 + 1 = 2 Soln: = 2(3) + 3(2) – 2 (6) = 6 + 6 -12 = 0 Soln: 2(p) + 1(3) – 5 (-2) = 0 2p + 3 +10 = 0 2p + 13 = 0 Soln: Soln: = 2 ( 1 ) + 1 ( -4) + 3 ( – 6 ) =    2 – 4 – 18 =   – 20 Soln: = 1(1) + 2(1) + 1(-3) = 0 = 1(7) + 1(-4) – 3(1) = 7…

## N – 2.1 – Vector Introduction – Exercise Problems with Solutions

Soln: Given Sol.:     Given Soln: The given triangle is an isosceles triangle.

## 2.1 – N – Vector Introduction – Exercise Problems

7. Show that the points whose position vectors 8. Prove that the points

## 2.3 APPLICATION OF SCALAR AND VECTOR PRODUCT

Application of Scalar Product Work done PART – B Example  : Soln: = 3 ( 2 ) + 5 ( – 1 ) + 7 ( 1 ) =    6  – 5  +  7 Work done = 8 units Example  : Soln: = 4 ( 2 ) + 9 ( – 7 ) + 4 ( 1 ) =    8  – 63  +  4     Work done  =  –51 units Work done  =  51 units  (by taking positive value) Example  : is displaced from the point ( 1, 1,  1…

## 2.2 PRODUCT OF VECTORS

SCALAR PRODUCT Definition:  Properties of Scalar Product: Example  : Soln: = 2(1) – 4 (6) + 8 (12) = 2 – 24 + 96 = 74 Example  : Soln: = 2(3) + 3(2) – 2 (6) = 6 + 6 -12 = 0 Soln: 3(-6) – 1(m) + 5 (4) = 0 -18 – m + 20 = 0 -m + 2 = 0 Soln: = 1(0) – 1(4) + 2 (2) = 0 = 0(-10) + 4(-2) + 2 = 0 – 8 + 8 = 0 = –…

## 2.1 VECTOR – INTRODUCTION

Vectors constitute one of the several Mathematical systems which can be usefully employed to provide mathematical handling for certain types of problems in Geometry, Mechanics and other branches of Applied Mathematics. Vectors facilitate mathematical study of such physical quantities as possess Direction in addition to Magnitude. Velocity of a particle, for example, is one such quantity. Physical quantities are broadly divided in two categories viz (a) Vector Quantities & (b) Scalar quantities. ( a ) Vector quantities : Any quantity, such as velocity, momentum, or force, that has both magnitude…