Skip to main content
Search IntMath
Close

450+ Math Lessons written by Math Professors and Teachers

5 Million+ Students Helped Each Year

1200+ Articles Written by Math Educators and Enthusiasts

Simplifying and Teaching Math for Over 23 Years

Tips, tricks, lessons, and tutoring to help reduce test anxiety and move to the top of the class.

2. Vector Addition (1-dimensional vectors)

Adding 1-dimensional Vectors

I am swimming downstream in a river.

swimming in a river

The speed of the river current is 0.25 m/s, as indicated by the length and direction of the blue arrow in the vector diagram.

Vector due to swimming

I swim downstream at the rate of 1 m/s, as indicated by the dark red arrow below. (It is `4` times the length of the river current vector, indicating that my swimming velocity is `4` times the velocity of the river current.)

River current vector

Our friends are on the riverbank watching me swim. They observe that I am moving quite quickly. My velocity is:

1 + 0.25 = 1.25 m/s.

The river is helping me to move quickly relative to the people watching. This is an example of vector addition.

We can show this on our diagram as follows:

Sum of river current and swimming vectors

The equivalent vector (1.25 m/s downstream) is shown in pink:

Sum of river current and swimming vectors

The diagram illustrates the boost that I am getting from the river current and demonstrates my total speed, relative to the riverbank, of:

1 + 0.25 = 1.25 m/s.

The Return Journey (Subtraction of Vectors)

To get back to my friends, I need to swim against the current so my speed relative to the people who are watching me will be less. My velocity relative to the river bank is now:

1 − 0.25 = 0.75 m/s.

The 2 vectors are now acting in opposite directions.

Swimming against the current

An equivalent way of drawing our 2 vectors is to put the tail of the current vector next to the tip of the swimming vector as follows:

Subtraction of vectors

My velocity relative to the people watching (0.75 m/s, upstream) is shown in pink:

Subtracting vectors

24x7 Tutor Chat

Tips, tricks, lessons, and tutoring to help reduce test anxiety and move to the top of the class.