1. Write a note on Physical Quantities.

The quantities in the form of which laws of physics are expressed, are called physical quantities. All the physical quantities can be divided into two categories:

1. Scalar physical quantities or scalars.
2. Vector physical quantities or vectors.

1. Scalars : The quantities which can be completely explained with their magnitude only are called Scalar Physical Quantities and they do not have any direction. Examples : Distance, Speed, Volume, etc.
2. Vector physical quantities : The quantities which have magnitude as well as direction are called Vector Physical Quantity. Examples : Displacement, Velocity, Acceleration, Force, etc.

2. What do you understand by a resultant vector?

The resultant of two or more vectors is that single vector whose effect is the same as that of the given vectors when they act simultaneously.

3. State the parallelogram law of vectors.

According to this law, if the vectors acting simultaneously at a point can be represented both in magnitude and direction by the two adjacent sides of a parallelogram, then the resultant is represented both in magnitude and direction by the diagonal of the parallelogram passing through that point.

4. State the triangle law of vector addition.

According to the ' triangle law of vectors ', if two vectors can be represented in magnitude and direction by the two sides of a triangle taken in the same order, then the resultant is represented completely, both in magnitude and direction, by the third side of the triangle taken in the opposite order.

In the below figure,

5. State three important properties of vectors addition.

1. Vector addition is commutative that is.

     2. Vector addition is distributive that is.

     3. Vector addition is associative that is.

6. Express the vector product of two vectors in terms of their rectangular components.

7. Can three vectors not in one plane give a zero resultant? Can four vectors do?

Three vectors not in one plane cannot give zero resultant. It is because the resultant of any two vectors which lie in one plane cannot cancel the effect of remaining third vector, not lying in the plane of the former two vectors. However , the resultant of four vectors not in one plane may be zero.

8. Calculate the magnitude of the vector metres.

9. What is a null vector?
A vector having zero magnitude is called null vector or zero vector. It is denoted by (arrow over the number zero). The need of zero vector arises because if we multiply a vector by zero, the result must be a vector. 0

Also,

10. What are co-initial and collinear vectors?
Two vectors having the same initial points re called co-initial vectors. are co-initial vectors as both of them start from O.

Two vectors which either act along the same line or along parallel lines are called collinear vectors.
In the below figure (i) and (ii), are collinear vectors.

11. Write a few properties of zero  vectors.

12. A particle has a displacement of 12 m towards east and 5 m towards north and 6 m vertically upwards. Find the magnitude of the sum of these displacements.

The resultant displacement due to 12 m towards east and 5 m towards north lies in the plane of paper and the angle between resultant displacement is 90^o and is given by,

Displacement 6 m is vertically upward perpendicular to the plane of paper. Therefore, the angle between R₁ and 6 m is 90^o. The resultant of these two (say R₂) will be,

13. What are unit vectors or base vectors?

The three unit vectors in the given figure along positive directions of x, y and z -axes are called unit vectors or base vectors. They are denoted by . They are together known as orthogonal triads or vectors.

14. Express the area of a parallelogram in terms of cross product of two vectors.

Consider a parallelogram with vectors forming its adjacent sides. If h be the height of the parallelogram, then the area of the parallelogram = A h

16. One of the rectangular components of velocity of 80 km/h is 40 km/h. find the other component.

u = 80 km/hr

Say, u_x  = 40 km/hr , u_y = ?
         u² = u_x² + u_y²
(80)² - (40)² = u_y²

17. Using the parallelogram law of vectors, find the magnitude and direction of the resultant in the following figure. Discuss cases for :

1. θ = 0^o
2. θ = 90^o
3. θ = 180^o

Thus, the magnitude of the resultant vector is equal to the sum of the magnitudes of the two given vectors and the resultant vector acts along the two vectors.

Thus, the magnitude of the resultant vector is equal to the difference in the magnitude of the given vectors and acts along the direction of the bigger vector.

18. State the polygon law of vector addition.

If a number of vectors can be represented both in magnitude and direction by the sides of a polygon taken in the same order, then the resultant is represented completely in magnitude and direction by the closing side of the polygon, taken in the opposite order.

In the figure below, vectors are acting at the point O. These vectors can be represented both in magnitude and direction by the sides respectively.

(By using triangle law of vectors)

 

19. It is easier to pull a lawn roller than to push it. Explain using the resolution of forces.

W is weight of the lawn roller. When pushed by applying a force at an angle θ, moves it forward while the apparent  weight becomes .

However, when pulled the apparent weight becomes,
Since the force of friction is directly proportional to normal reaction (equal to apparent weight of the roller), it is more when it is pushed than when it is pulled.

20. Define scalar product of two vectors. Give one example.

The scalar product or dot product of two vectors

where A and B are magnitudes of and θ is the smaller angle between the two, the vectors being placed tail to tail. This product is also called inner product. The dot product of force and displacement is work done, which is scalar.