# Vector multiplication and division

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• jamiebean

#### jamiebean

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

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?

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

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.

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##.