Difference between scalars and vectors

[brandy]

i know that a scalar quantity is something with magnitude and a vector is something with magnitude and direction but how do u apply that in maths. what's the difference between scalar multiplication and vector multiplication...?
if its not too hard could u dumb it down. am not all that smart.
please and thanku.

 

[Gib Z]

Scalar Multiplication is just the multiplication of scalars, ordinary multiplication that you already know of =]. The ordinary numbers you already now are all scalars, they have a magnitude. They also have a direction, as we can see if we draw a number line. The positive numbers are in the right direction, and we denote the left direction with the negative numbers.

The direction of a general Vector can be must more complex than that, and can't just have a simple +/- sign to work it out. There are two main operations we call vector multiplication, the Dot product and the cross product. As we have just discussed, scalars are vectors with very simple directions. The dot product and cross product of two general vectors do not always have the same result, but when with scalars are always the same, and also equate to normal multiplication. This is why sometimes we use a dot to denote scalar multiplication instead of a cross.

The direction in a vector is very important when being applied in physical situations. For example, take the scalar quantity - speed. The speed of two separate objects may be both 10m/s. This isn't too much useful. However, the velocity of these two objects may be 10m/s North and 10m/s South , which gives us more information about what's going on.

 

[brandy]

so for 1*2 is scalar multiplication? and (1,2)*(2,3) is vector? well wat about dot product and cross product. for (1,2);(2,3) would u go 1*2,2*3 or 1*2+2*3

 

[ice109]

the "cross product" is only defined for 3 vectors, the dot product is the latter of what you put down.

 

[robphy]

One should try to distinguish
- "multiplication of scalars" (i.e. "ordinary" multiplication)
- the more-ambiguous "scalar multiplication", which may refer to the multiplication of a scalar and a vector (i.e. "scaling" a vector by changing its magnitude without changing its direction), and
- "scalar product ["dot product" of two vectors]".