# Define Scalars And Vector

Q.1: Define scalar and vector quantities and give five examples of each?

Ans: SCALAR QUANTITIES:

Physical quantities which have magnitude and units but there is no need of direction to describe them are called scalar quantities. Scalar quantities can be solved by simple arithmetic rules. They can add, subtract, multiply and divide easily.

Examples:

Mass, length, time, speed, distance, volume, temperature, heat, energy, pressure, power, etc.

VECTOR QUANTITIES:

Physical quantities which have magnitude and units but we need particular direction to completely specified them is called vector quantities. Vectors are added, subtracted, multiplied and divided by the rules of vector algebra.

Examples:

Velocity, displacement, acceleration, force, weight, torque or moment, momentum. etc.

Q.2: How we represent a vector quantities?

Ans: VECTOR REPRESENTATION:

We can represent vector quantities by an arrow. The length of the arrow represents the magnitude and the arrow head represents the direction.

Q.3: Define multiplication of a vector by a number?

Ans: MULTIPLICATION Of A VECTOR:

When a vector is multiplied by a number it remains a vector quantity. If the number, say “n’, is positive the new vector has a magnitude “n times the magnitude of the original vector and its direction remains the same.

A line segment making an angle of 30° with x-axis gives magnitude and direction of velocity of the boat by considering the x-axis no parallel to the bank of the river.

For example, a vector F of 2cem length will become of 4cm if multiplied by 2 and a vector F of ; cm multiplied by 2 will be 1 cm. When a vector is multiplied by a negative number say -2 , the new vector becomes two times the magnitude of the original vector and its direction is opposite to it.

Q.4: Define negative of a vector?

Ans: If we have two vectors of same magnitude but one of them has opposite direction to the first vector, it will be the negative of the first vector. The representative lines of a vector and negative vector are equal and parallel to each other but their heads are in opposite direction.

Q.5: What do you mean by resultant vector?

Ans: The process of combining two or more than two vectors to produce a single vector having the combine effect of all the vectors is called the resultant vector.

R=A+B

Ans: Two or more than two vectors can be added by head to tail rule in such a way that we put the tail of the second vector to the head of the first vector and the tail of the third vector to the head of the second vector and so on. This method of adding vectors is known as head-to-tail rule of vector addition. There are two methods of adding vectors by head-to-tail rule.

Vector Acting Along The Same Line:

The resultant of a number of vector which are acting along the same line is a new vector whose magnitude is the sum of the magnitude of all the given vectors and whose direction is same as that of the given vector.

Vectors Acting Along Different Lines:

The resultant of two vector acting along different line can be obtained by drawing the vectors lines in such away that the tail of one coincide with the head of the other the line joining their free ends will give the resultant vectors.

Q.7: Define subtraction of a vector? Explain it with one example?

Ans: In order to subtract a vector from another vector the sign of the vector be subtracted is changed and then added to the other vector.

Example:

If a vector B is to be subtracted from a vector A then A — Bis found by adding A and (8). The subtraction of vectors are shown in the given figure. Vectors A.B and (-B) are represented by the lines.

R=A+(-B)=4=8

Q.8: Define trigonometric ratios?

Ans: Trigonometry is an important branch of mathematics. it Cc deals with the relations between angles and sides of triangles. A right triangle is one that contains a 90° angle. Here AB and BC are the adjacent and opposite sides to the angle “6” and are generally called base and perpendicular respectively. The side opposite to the right angle is called hypotenuse. The three most important a @ (|

trigonometric function of an angle are called sine, cosine, A B and tangent. They are briefly written as sin, cos and tan.The trigonometric ratios gives the ratios between the various sides of a right triangle. Here side AB is base or side adjacent to “@” and side AC is hypotenuse which is always opposite the right angle in a right triangle. The common ratios are:

Q.1: Define Parallel forces?

Ans: The parallel forces can be define as, “when a number of forces act on a body and if their directions are parallel they are called parallel forces.”

Q.2: What do you understand by two like and unlike parallel forces?

Ans: LIKE PARALLEL FORCES:

If two parallel force have same direction they are called like parallel forces.

Examples:

“Consider two like parallel forces F1 and F2 acting on a body at “A” and “B”. Suppose R is the resultant force of f1 and f2 then

Fy and F, then | . acting on a body

R=F1 + F2

UNLIKE PARALLEL FORCES:

If two parallel forces have opposite directions they are called unlike parallel forces. ‘

Examples:

“Consider two unlike parallel forces F1, and F2, acting on a body at point “A” and “B”. Suppose R is the resultant force of F1, and F2, Here F1, is greater than F2”

R=F1,- F2,