Vector Subtraction



In this lesson, we will learn how to subtract vectors by adding its negative, how to subtract vectors geometrically using the head-to-tail method and how to subtract vectors using their components.

Related Topics:
Vector Addition

More lessons on Vectors

How to subtract Vectors

Subtracting a vector is the same as adding its negative.
The difference of the vectors p and q is the sum of p and –q.
p q = p + (–q)

Example:

Subtract the vector v from the vector u.


Solution:

u v = u + (–v)

Change the direction of vector v to get the vector –v.

Check: The column vector should represent the vector that was drawn.



Vector Subtraction
u - v = u + (-v)
Since we know how to add vectors and multiply by negative one, we can also subtract vectors.



Geometric subtraction of two vectors





An illustration of how to subtract vectors graphically.





Subtracting vectors.





Subtracting Vectors
Subtract the following vectors (B - A)
A = 5.0 m at 40 degrees west of North
B = 2.5 m south



Vector subtraction including boat example
Introduction to 'head to tail' vector subtraction in the geometric sense. This is then applied to an example of working out a boat's velocity relative to water given the velocity of the current and the velocity of the boat relative to land are both known.



How to subtract vectors using their components

Subtracting Vectors in Component Form



Adding and subtracting component form vectors







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