Question

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How does multiplying a vector by a scalar value of -pi/4 change the vector?

Answer 1

A vector has length (magnitude) and direction.

Multiplying a vector by a scalar can alter both its length and its direction.

Specifically, you are multiplying by
`- ( \pi )/(4)`.
When you multiply a vector by a negative as in this case the direction changes.

Next when we multiply by a quantity greater than 1 the vector's length increases. When we multiply by a quantity less than 1 the vector's length decreases. Here you are multiplying by a quantity less than 1. For the sake of getting an estimate pi is approximately 3.14 so dividing that by 4 gives you a quantity less than 1.

So multiplying by
`-( \pi )/(4)` will have the following effects on the vector:
It will face the opposite direction and it will be shorter (have less magnitude). Specifically the magnitude will be
`( \pi )/(4)` of what it was before.