Question

How does multiplying a vector by a scalar value of 2pi change the vector?

A.) The vector will change direction and increase in magnitude.
B.) The vector will change direction and decrease in magnitude.
C.) The vector will not change direction but will increase in magnitude.
D.) The vector will not change direction but will decrease in magnitude.

Answer 1

This is a problem of geometry. So, a scalar has magnitude (size) only. Therefore, we can conclude that ta scalar is just a number. If we multiply a vector by a scalar it is called scaling a vector, because we change how big or small the vector is. Given that 2π is a positive scalar then the answer is:

C) The vector will not change direction but will increase in magnitude.

This is true because:


`2 \pi \ \textgreater \ 1`