Scalar and vectors with solved examples ppt

scalars and vectors

1. Topics Covered 1. Scalars 2. Vectors 3. Vector Representation 4. Properties of Vectors

2. Scalars Scalars are quantities that are described completely by magnitude only. They do not have any direction. Examples include mass, temperature, time, and energy. Scalars follow ordinary rules of arithmetic operations.

3. Vectors - Introduction Vectors are quantities that have both magnitude and direction. They are graphically represented by arrows. Examples: displacement, velocity, acceleration, force. Notation: Bold letters (A) or with an arrow above (→AB).

4. Vector Representation A vector is represented by a directed line segment. The length of the arrow indicates the magnitude. The direction of the arrow shows the direction of the vector. Example: Vector AB from point A(x1,y1) to B(x2,y2).

5. Properties of Vectors 1. Equal Vectors: Same magnitude and same direction. 2. Zero Vector: Magnitude zero, no specific direction. 3. Unit Vector: A vector with magnitude 1. Commonly represented as î, ĵ, and k̂ in 3D.

6. Scalar Example 1 Mass: 50 kg Explanation: Scalar has only magnitude.

7. Scalar Example 2 Temperature: 25°C Explanation: No direction is associated.

8. Scalar Example 3 Time: 10 seconds Explanation: It only expresses magnitude.

9. Vector Example 1 Velocity: 60 km/h east Explanation: Has both magnitude and direction.

10. Vector Example 2 Force: 20 N upward Explanation: Expressed by magnitude and direction.

11. Vector Example 3 Displacement: 5 km north Explanation: Shows distance and direction.

12. Vector Property Example 1 Equal Vectors: Two vectors with same magnitude and direction. Example: 5 N east and another 5 N east.

13. Vector Property Example 2 Zero Vector: Magnitude = 0. Example: A vector from a point to itself.

14. Vector Property Example 3 Unit Vector: Vector with magnitude 1. Example: î (1,0) or ĵ (0,1).

15. Vector Representation Example 1 Vector AB from A(2,3) to B(6,7). Components: (6-2, 7-3) = (4,4).

16. Vector Representation Example 2 Displacement vector: 3i + 4j. Magnitude = √(3²+4²) = 5.

17. Vector Representation Example 3 Arrow diagram: Direction shows orientation. Length of arrow shows magnitude.

18. MCQs on Scalars Q1: Which of the following is a scalar? a) Velocity b) Force c) Mass d) Displacement Answer: c) Mass Q2: Which property applies to scalars? a) Both magnitude and direction b) Only magnitude c) Only direction d) Neither Answer: b) Only magnitude

19. MCQs on Vectors Q1: Which of the following is a vector? a) Time b) Speed c) Velocity d) Temperature Answer: c) Velocity Q2: The graphical representation of a vector is: a) A point b) A line c) An arrow d) A circle Answer: c) An arrow

20. MCQs on Vector Properties Q1: A vector with magnitude 0 is called: a) Equal vector b) Unit vector c) Zero vector d) None Answer: c) Zero vector Q2: A unit vector has magnitude: a) 0 b) 1 c) Any value d) Undefined Answer: b) 1

21. MCQs on Vector Representation Q1: The components of vector AB if A(1,2), B(4,6) are: a) (3,4) b) (5,5) c) (2,3) d) (4,2) Answer: a) (3,4) Q2: If a vector is represented as 7i + 24j, its magnitude is: a) 25 b) 31 c) 17 d) 20 Answer: a) 25

22. Outcome of Today's Session 1. Differentiated between scalars and vectors. 2. Learned how to represent vectors graphically and in component form. 3. Understood properties of vectors such as equal, zero, and unit vectors. 4. Practiced examples for better clarity. 5. Answered MCQs to strengthen understanding.