Vector Subtraction is Explained In-detail

There are several parallels between vectors and scalars. Vector subtraction is no exception. Especially, vector subtraction is:

” The negative of an additional vector adds a vector.”

From the definition mentioned above, it is evident that vector subtraction suggests the addition of negative vectors. Therefore, it is essential to examine negative vectors before learning vector subtraction.

Moreover, a negative vector is obtained when multiplying an offered vector by -1. This reverses the direction of the vector.

Let’s say A is a vector aiming from entrusted to the right. Multiplying the vector A by -1 offers us -A, which is vector A’s negative. Although the size of the two vectors An and also– A will stay the same, the negative vector– A will direct from right to left.

In this subject, we will further talk about adhering to facets of vector subtraction:

Exactly How to Subtract Vectors

Subtracting Vectors Graphically

How to Subtract Vectors

We know that two vectors, An and B, can be totalled using vector addition. Therefore, the resultant vector can be composed as R = A + B. At the same time, if we go for the subtraction of two vectors, An, as well as B, is expressed mathematically as:

R = A– B.

Alternatively as.

R = A +(- B).

Therefore, subtracting both vectors coincides with adding vector An and vector B’s negative (i.e., B). The vectors B and– B will certainly have the same size. However, -B’s direction will undoubtedly be opposite to that of vector B.

Vector subtraction likewise functions when both vectors are given up element kind or as column vectors. If B = (bx1, by1) and A = (ax1, ay1), the disparity between the two is.

R = A– B.

You can share the horizontal and vertical parts of the resultant vector R.

Rx = ax1– bx1.


Ry = ay1– by1.

Hence, you can compute the resultant vector by calculating the difference between the original vectors’ corresponding horizontal and vertical elements.

Subtracting Vectors Graphically.

Graphically, the head-to-tail policy that uses vector addition can be adjusted for vector subtraction. For instance, look at the two vectors Q and P, as depicted in the diagram. Note that the vector– Q is acquired by reversing the direction of Q.

About Vectors in brief

A vector can be specified as a quantity, measurement, or thing with both a magnitude and direction. It is one of the most essential and fundamental concepts in Physics that locates its applications in almost all the subject branches. A vector can be imagined geometrically as a directed line section. The length of the line segment represents the size of the vector, and the arrowhead represents the direction of the vector. The direction of any vector is defined from its tail to its head, where the arrow is.

Read Also: Area of a Polygon – Learn with Examples

Most typical examples of vector quantities include force, rate, velocity, displacement, energy, electrical area, and so on. You can put on fundamental algebraic operations vectors, yet they have their guidelines for these operations. We can not add or subtract vectors like we add or subtract numbers. Vectors also have directions, so this has to be considered.

What is Vector Subtraction?

The vector subtraction of 2 vectors, an and b, is stood for by a – b and includes the vector b negative to the vector a., i.e., a – b = a + (- b). Hence, the subtraction of vectors involves the addition of vectors and also the negative of a vector. The outcome of vector subtraction is once again a vector. The following are the regulations for subtracting vectors:

You should execute it between two vectors (not between one vector and one scalar).

Both vectors in the subtraction ought to represent the same physical quantity.

Let us comprehend just how to subtract vectors graphically in the approaching sections.

Vector Subtraction by Parallelogram Law

We mean that an and b are two vectors. How can we translate the subtraction of these vectors graphically? That is, what significance do we affix to a – b? To begin with, we consider that a – b will be a vector which, when contributed to b, must return a., i.e.,

( a – b) + b = a

However, how do we identify the vector a – b, given the vectors an and b? The following number reveals vectors an and b (we have attracted them to co-initial).

When employing the parallelogram law of vector addition, we can identify the vector as complies with. We analyze a – b as a + (- b), the vector sum of an and − b. Currently, we turn around vector b, and after that, including an as well as -b using the parallelogram law.

Graphically subtract the offered vectors An and B, shown in the image listed below, using the head-to-tail technique.


We initially draw the vector B negative by reversing its direction, i.e., -B. Subsequently, we add the vectors An and– B using the head-to-tail method.

We top place the given vectors An and– B such that the tail of the vector -B links to the head of vector A as received in the image below. Next off, to locate their sum, we develop a resultant vector R. Hence, it links vector A tail to the head of a vector– B. Mathematically, the consequent can be shared as:

R = A + (- B).