Physics Complete: VECTORS CONCEPTS

1.Physical quantities are mainly classified into two types a) Scalars b) Vectors .

2. Scalar quantities re those which have only magnitude.

3. Physical quantities which have both magnitude and direction are called vectors and they should satisfy the parallelogram law of vector addition.

4. Mathematically any directed line segment is called a vector. It has three characteristics.

a) Support (base)
b) Sense (direction)
c) Length (mangnitude or modulus)

5. The magnitude of a vector is a scalar.

6. Electric current, velocity of light have both magnitude and direction but they do not obey the laws of vector addition. Hence they are scalars.

DIFFERENT TYPES OF VECTORS

7. EQUAL VECTORS: Two vectors are said to be equal when their magnitude and direction are equal.

8. NEGATIVE VECTOR: Negative vectors are those which are equal in magnitude but opposite in direction.

9. NULL VECTOR (ZERO VECTOR): It is a vector whose magnitude zero and direction is unspecified.

Examples :

a) Displacement after one complete revolution.

b) Velocity of vertically projected body at the highest point.

10. UNIT VECTOR : It is a vector whose magnitude is unity. A unit vector parallel to a given vector R is given by R ˆr = R

11. REAL VECTOR OR POLAR VECTOR : If the direction of a vector is independent of the coordinate system, then it is called a polar vector.

Example : linear velocity, linear momentum, force, etc.

12. PSEUDO VECTOR: Vectors associated with rotation about an axis and whose direction is changed when the co-ordinate system is changed from left to right, are called axial vectors (or) pseudo vectors.

Example : Torque, Angular momentum, Angular velocity, etc.

13. POSITION VECTOR: It is a vector that represents the position of a particle with respect to the origin of a co-ordinate system. The Position Vection of a point (x, y, z) is r = x i+yj+zk .

ADDITION OF VECTORS

14. There are three laws of addition of vectors.

a) Commutative law : A + B = B + A

b) Associative law : A + (B+C) = (A + B) + C

c) Distributive law : m(A + B) = mA + mB where m is a scalar

RESULTANT OF NUMBER OF VECTORS

15. Resultant is a single vector that gives the total effect of number of vectors.

16. Resultant can be found by using a) Triangle law of vectors b) Parallelogram law of vectors c) Polygon law of vectors .

17. TRIANGLE LAW OF VECTORS: If two given vectors are represented both in magnitude and direction by the two adjacent sides of a triangle, then closing side (third side) taken in the reverse order will give the resultant both in magnitude and direction.

APPLICATIONS OF TRIANGLE LAW :

a) MOTION OF A BOAT CROSSING THE RIVER IN SHORTEST TIME :

If velocities of boat and river are represented with B and R subscripts with V then to cross the river in shortest time, the boat is to be rowed across the river i.e., along normal to the banks of the river.