Mathematics - Vector Algebra

In Algebra, Vector Algebra is considered as an essential topic. In this, the vector quantities are measured. There are two types of physical quantities like vector and scalar. Several Algebraic operations perform on vectors and vector spaces. An arrow that signifies the direction (→) represents a Vector, and its length shows the Magnitude.

Vector Algebra Operations

Algebra is performed with the help of Arithmetic operations like addition, multiplication, subtraction and so on.

Addition of Vectors

If we consider the two vectors, P & Q, the sum of two vectors can be performed when the tailor vector Q meets with Vector A's head.

  • Commutative Law: P+Q=Q+P
  • Associative Law: P+ (Q + R) = (P + Q) + R

Subtraction of Vectors

In Subtraction, the Vector's direction gets reversed, and then the addition is performed on both the vectors.

P + Q = P + (-Q)

Multiplication of Vectors

Suppose we multiply the K with a vector A. It will give a scalar multiplication by kA. In case K is positive, the direction of vector kA will be the same as vector A.

Vector Algebra Example

Question: Find the dot product of vectors P (1, 2, -6) and Q (1, −2, 4).

Ans: As per the vector algebra definition of the dot product, we know;

P.Q = P1Q1 + P2Q2 + P3Q3 +… PnQn


P.Q = 1. 1 + 2. (-2) + (-6). 4

= 1 - 4 - 24

= - 27