Question

A vector quantity has:
A) Only magnitude
B) Only direction
C) Both magnitude and direction
D) Neither magnitude nor direction

Answer 1

Hint: In order to solve this problem it is very important to be very sure of what we mean when we talk about magnitude and what we mean when we talk about direction. When we are well aware of the basic knowledge of quantities we can easily answer this question.

Complete step by step answer:
A physical quantity which can be specified completely by giving a single number and the appropriate unit alongside it is known as a scalar quantity. Scalar quantities that have the same physical units can be added or subtracted according to the strict mathematical rules of algebra for numbers.

There are a lot of physical quantities which cannot be described by just a single number of physical units. For example in order to fetch a ball which is thrown it is not only important to know the speed with which it is thrown but also the direction in which it is thrown so that it is easier to locate the ball. Physical quantities which are specified completely by giving a number of units (magnitude) and a direction alongside it are known as vector quantities.
Thus we see that a vector quantity has both magnitude and direction.

Thus, we see that the correct answer to this question is (C).

Note: The most common examples of vector quantities are displacement, the velocity, position, force, and torque on an object. Mathematically speaking, physical vector quantities are represented by mathematical objects known as vectors. We can add or subtract two different vector quantities, and we can also multiply a vector quantity by a scalar quantity or also by another vector quantity, but we cannot divide it by a vector quantity. The operation of division by a vector quantity is not defined mathematically.