﻿ Definition of Addition of Vectors | Define Addition of Vectors - Pre-Calculus - Free Math Dictionary Online

## Definition of Addition of Vectors

• Adding two or more vectors to form a single resultant vector is known as Addition of Vectors.

• If two vectors have the same direction, then the sum of these two vectors is equal to the sum of their magnitudes, in the same direction.
• If the two vectors are in opposite directions, then the resultant of the vectors is the difference of the magnitude of the two vectors and is in the direction of the greater vector.

### Examples of Addition of Vectors

• To find the sum of the vectors of and, they are placed tail to tail to form two adjacent sides of a parallelogram and the diagonal gives the sum of the vectors and . This is also called as 'parallelogram rule of vector addition'.
• If the vector is represented in Cartesian coordinate, then the sum of the vectors is found by adding the vector components.
The sum of the vectors u = <- 3,="" 4=""> and v = <4, 6=""> is
u + v = <- 3="" +="" 4,="" 4="" +="" 6="">
= <1, 10="">

### Solved Example on Addition of Vectors

#### Let = <- 5,8=""> and = <8, 10="">. Which of the following is the component form of the vector + ?

##### Choices:
• A. <3, 18="">
• B. <18, 13="">
• C. <13, 18="">
• D. <18, 3="">

#### Solution:

• Step 1: = <- 5,="" 8=""> and = <8, 10="">
• Step 2: +
= <- 5,="" 8=""> + <8, 10=""> [Use the definition of sum of vectors.]
Step 3: = <- 5="" +="" 8,="" 8="" +="" 10="">
Step 4: = <3, 18="">
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