Question

Which of the following is false regarding vectors?
A. The magnitude of a vector is always a scalar.
B. Each component of a vector is always a scalar.
C. Two vectors having different magnitudes cannot have their resultant zero.
D. Vectors obey triangle law of definition.

Answer 1

Physical quantities can be both scalar and vector. Scalar quantities are the ones with only magnitude but no direction like mass, energy etc. Vector quantities are the ones with both magnitude and direction like force, velocity etc. A vector is usually represented like a ray, a straight line with an arrow head pointing towards the direction of the vector. A negative of a vector is nothing but the same vector with the equal magnitude but in the opposite direction. Using the mentioned definition, we can solve the question by reading every option one by one.

Complete answer:
Let’s start by examining every option.
Option A: The magnitude of a vector is always a scalar.
The magnitude of a vector quantity is just a real number, an integer or a decimal. Hence, the magnitude of a vector is always scalar.

Option B: Each component of a vector is always a scalar.
When we say a component of a vector, we mean every part of a two-dimensional vector. The combined influence of the two vectors will give us the original vector.

Every component of a vector is also a vector. We can never get a vector quantity by adding a scalar quantity to a vector.

Option C: Two vectors having different magnitudes cannot have their resultant zero.
No. Two vectors with different magnitudes can never give a resultant zero no matter in which direction they are. The resultant of two vectors will only be zero when they have the same magnitude and are in opposite directions. But three or more vectors can have a resultant of zero even if they have different magnitudes.

Option D: Vectors obey the triangle law of definition.
Triangle law of addition states that when two vectors are represented as two sides of a triangle with the order of magnitude and direction, the third side represents the magnitude and direction of the resultant vector. Therefore, they obey the triangle law of addition.

Where $\overrightarrow A + \overrightarrow B = \overrightarrow C$

Therefore, the only false option is B.

Note: Vectors are useful in algebra and also in showing physical quantities with both magnitude and direction like acceleration, gravity etc. Along with triangle law of addition, there is parallelogram of addition which means that if two vectors act along two adjacent sides of a parallelogram away from the common vertex, the resultant is represented by the diagonal vector.

Where $\overrightarrow {AC} = \overrightarrow {AB} + \overrightarrow {AD}$.