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Welcome to our Physics lesson on Division of a vector by a scalar as multiplication with the inverse, this is the second lesson of our suite of physics lessons covering the topic of Multiplication of a Vector by a Scalar, you can find links to the other lessons within this tutorial and access additional physics learning resources below this lesson.
In the previous article "Addition and Subtraction of Vectors", we have pointed out that in algebra there are only two basic operators: addition and multiplication. Subtraction and Division are considered as subsidiaries of these two basic operators. Thus, subtraction is regarded as "addition with the opposite" while division as "multiplication with the inverse".
Given this, it is obvious that if we have a vector u⃗ and we want to obtain a new vector v⃗ which has the same direction but is N-times smaller, we can mathematically express this statement in two ways:
For example, the Newton's Second Law states, "the acceleration a⃗ an object acquires due to the action of a force F⃗ is proportional to the force and inversely proportional to the mass m of the object (acceleration and force are both vectors while mass is a scalar).
Mathematically, this law can be written in two ways:
Therefore, either we divide the vector F⃗ with the scalar m to obtain another vector a⃗, or we multiply the vector F⃗ to the inverse of the scalar m (1/m) to obtain the same vector a⃗.
An object is pulled horizontally due North by a 120N force. As a result, it accelerates by 1.5 m/s2.
What is the object's mass in kg?
In what direction is the object accelerating?
a. Using the Newton's Second Law as mentioned above, we obtain
b. Given that when multiply a vector by a scalar the result is a new vector, which has the same direction as the original vector, the direction of acceleration is due North as well.
You have reach the end of Physics lesson 2.3.2 Division of a vector by a scalar as multiplication with the inverse. There are 4 lessons in this physics tutorial covering Multiplication of a Vector by a Scalar, you can access all the lessons from this tutorial below.
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