# How do I multiply a vector by a scalar?

Dec 27, 2014

The multiplication of a vector by a scalar can affect the MODULUS (the size) and can affect the DIRECTION of your vector:
Multiplication by a positive number other than 1 changes the magnitude of the vector but not its direction.
Multiplication by –1 reverses its direction but doesn’t change its magnitude.
Multiplication by any other negative number both reverses the direction of the vector and changes its magnitude.

For example:
given the vector $\vec{v}$ of modulus equal to 3 units multiply by 2 makes the module become 6. Multiply by -2 vector $\vec{v}$ changes also its direction:
Graphically:

If your vector is given in component form you simply multiply each component by the scalar:
For example:
$\vec{v} = 4 \vec{i} + 3 \vec{j}$
$2 \cdot \vec{v} = 8 \vec{i} + 6 \vec{j}$
The ending result is again that the modulus is multiplied by 2!!!
Check the result by plotting the two vectors.