Question

Select the statements that describe a vector. Check all that apply.
Vectors have a size only.
Vectors have a size and a direction.
Vectors are indicated with arrows.
Vectors can have only positive values.
Vectors can have positive or negative values.

Answer 1

By definition, vectors are quantities that have magnitude (positive or negative) and direction.
Graphically, they are illustrated by directed line segments, with arrows that indicate the direction.

Evaluate the given statements.
1. Vectors have a size only.  FALSE
2. Vectors have a size and a direction. TRUE
3. Vectors are indicated with arrows. TRUE
4. Vectors can have only positive values. FALSE
5. Vectors can have positive or negative values. TRUE

Answer 2

The vectors are the mathematical entity which defines any quantity with direction and magnitude, such that any specific direction is positive and opposite direction is negative. Therefore, the statements (b), (c) and (e) are correct.

• The quantities having the magnitude as well as the direction for their complete definition are known as Vectors or Vector quantities.
• The vectors are determined by means of magnitude which can be the value of size or length of any object.
• The direction of vectors are determined through the positive and negative signs (Negative sign denotes the opposite direction).

(a) Since, vectors are dependent on magnitude along with direction. So, the statement, "Vectors have a size only" is incorrect.

(b) Vectors are defined by magnitude and direction. Hence, the statement "Vectors have a size and a direction" is correct.

(c) Mathematically, vectors are represented by arrows on the variable. For example: ₋  $\vec {a}$  is a vector.  Hence, the statement 'Vectors are indicated with arrows" is correct.

(d) Vectors are direction direction dependent which can be positive or negative as per the sign convention. Hence, the statement "Vectors can have only positive values" is incorrect.

(e) As per the above explanation, vectors may have both positive and negative value dependent on direction. So, the statement  "Vectors can have positive or negative values" is correct.

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