Question

So I have a question on vectors and scalars. How would you convert a scalar into a vector and vice versa?

Answer 1

a scalar is a value; it can be represented by a number or by a function.
however, regardless, what distinguishes it from a vector is that it does not have a direction
examples are mass, energy, work, constants such as G, mu-knot, and epsilon-knot

a vector has both a value and a direction
examples of vectors are position, velocity, acceleration, force

if you multiply two vectors, depending on how you multiply them, you can either get a vector or scalar

a dot product of two vectors give a scalar
the cross product of two vectors give a vector

I'm unaware however of how to convert a scalar to a vector

Answer 2

@LastDayWork
is what @jalega31 asking even possible?

Answer 3

I think @jalega31 is asking about the resolution of vectors -
Like V = Vx i + Vy j + Vz k
(Note: x, y, z are subscript; i, j, k are unit vectors)
Some books call Vx, Vy, Vz to be scalar components of the vector V

In other words; a vector can be broken into a (scalar) magnitude and a (vector) direction.

But, converting a scalar quantity into a vector quantity and vice-versa is not possible.

Answer 4

Oh really? My professor was just teaching this last week, I guess. This is the equation he put up, if it even made sense: (vector)a * k = (vector) b and then he wrote a * (vector) k= (vector) b

Answer 5

I'm not sure if that made sense, but if anything I'll ask again tomorrow if my prof. is available.

Answer 6

Were a, k and b related to any physical quantity ??

Answer 7

It did not specify in any of my notes. Sorry about that.

Answer 8

Although I do appreciate the answers and comments.

Answer 9

Was it a part of some question ? If yes, can you upload the complete question ?

Answer 10

No, it was not part of a question at all. It was just like a side note that he wrote on the side.

Answer 11

"... (vector)a * k = (vector) b and then he wrote a * (vector) k= (vector) b ..."

The statement ^^ implicitly assume that vector a, k, b are parallel vectors. (Maybe your professor expected you to deduce this fact)

Let A, K, B represent vectors and a, k, b their corresponding magnitudes.
Then the above statement simply means -
A * k = B
a * K = B

Does that ^^ makes sense ??

Answer 12

wait ok ok. i think it's making sense to me now.

Answer 13

actually what you just said, @LastDayWork I don't think they're parallel vectors, I think they're identical vectors...

Answer 14

@roadjester If by "identical" you mean that the vectors are in the same direction - technically yes; but some people may write a<0 or k<0; so I thought using "parallel" would be a safe bet. :)

BTW, we use the term "identical" to imply that the (free) vectors are equal.

Answer 15

Thank you guys for clearing this up for me :)

Answer 16

No problem

Answer 17

Convert the scalar speed into the vector velocity by
including the direction.