No.38

Adding Vectors

And here is how to add two vectors after breaking them into x and y parts:

The vector (8,13) and the vector (26,7) add up to the vector (34,20)

Example: add the vectors a = (8,13) and b = (26,7)

c = a + b

c = (8,13) + (26,7) = (8+26,13+7) = (34,20)

Subtracting Vectors

Remember: to subtract, first reverse the vector you want to subtract, then add.

Example: subtract k = (4,5) from v = (12,2)

a = v + -k

a = (12,2) + -(4,5) = (12,2) + (-4,-5) = (12-4,2-5) = (8,-3)

Magnitude of a Vector

The magnitude of a vector is shown by two vertical bars on either side of the vector:

|a|

OR it can be written with double vertical bars (so as not to confuse it with absolute value):

||a||

You can use Pythagoras' theorem to calculate it:

|a| = √( x² + y² )

A vector with magnitude 1 is called a Unit Vector.

Vector vs Scalar

When using vectors we call an ordinary number a "scalar".

Scalar: just a number (like 7 or -0.32) ... definitely not a vector.

A vector is often written in bold,

so c is a vector, and it has magnitude and direction

but c is just a value, like 3 or 12.4

Example: kb is actually the scalar k times the vector b.