Question

Good Morning!

We know that vectors have two basic operations their are scalar multiplication and vector
addition.
Can someone explain to me the difference of both of them?

Answer 1

So if you have vectors v and 2v
vector addition would give 3v
what would multiplication give?

Answer 2

if you have these two vectors

Answer 3

vector addition would give you this resultant vector



you use either the head-to-tip rule or parallelogram law to add them

Answer 4

scalar multiplication would scale any vector

ex: if you have a vector v and you multiply it by 2, you get 2v and you are doubling the vector's length

Answer 5

Suppose that u, v, and w are any vectors in R^2 and c
and d are scalars, then
v + w = w + v, we are saying that the addition
of vectors is commutative, we may interchange the summands and the result
is unchanged right?