Multiplying a vector by a non-zero scalar always produces a parallel vector means?

I dont get what the title means.

What is a non-zero scalar just any value i.e. 4.

so 4(4i+j) = 16i + 4j gives a parallel vector smh.

Parallel to the initial vector?

A scalar is just a single number (like 4), whereas a vector has more than one component (i and j). Parallel vectors are just vectors that are pointing in the same direction



In the above, both are pointing in the same direction, so they're parallel, it doesn't matter that one of them is twice the other.

Ofc, so the vector will have another vector which is a scalar multiple of itself, so it will point in the same direction. Is that correct?

Thank you for the visual interpretation.

Yeah that's all it is, if you multiply a vector by a number it doesn't change the direction, just the size of it.

The only thing is, if you multiply by a negative number it'll point in the opposite direction, which is called "antiparallel". But that's probably not very important.