High School Vector multiplication and division

[jamiebean]

what is the use of multiplying and dividing a vector by a scalar?

 

[A.T.]

what is the use of multiplying and dividing a vector by a scalar?

Is this a math or a physics question? If the later, what examples to you know from physics?

 

[Ssnow]

Multiplying or dividing a vector by a scalar is possible to modify the module of the vector increasing or decreasing it. For example if you have the vector $\vec{v}=(1,1)$ on the plane and the scalar $\alpha=2$ the result of the product (scalar-vector) is the vector $\vec{w}=\alpha\cdot \vec{v}=2\cdot (1,1)=(2,2)$. The module of $\vec{w}$ is equal to $2\sqrt{2}$ that is bigger respect to the module of $\vec{v}$ that is $\sqrt{2}$ (in this case in order to have the module you can use the Pythagorean theorem so $|\vec{w}|=\sqrt{2^2+2^2}=\sqrt{8}=2\sqrt{2}$ and $|\vec{v}|=\sqrt{1^2+1^2}=\sqrt{2}$).

Ssnow

 

[Drakkith]

what is the use of multiplying and dividing a vector by a scalar?

I am traveling 30 mph to the west in a car on the way to my grandmother's house. The trip is taking a long time and I want to cut the remaining travel time in half.
I can therefor multiply my velocity vector by 2 to get the new vector of 60 mph to the west.

 

[Herman Trivilino]

what is the use of multiplying and dividing a vector by a scalar?

They scale the magnitude of the vector. For example, a scalar with a value of $2$ can be used to scale the magnitude up by a factor of $2$ or down by a factor of $2$, by multiplying or dividing, respectively, by $2$.