The Student Room Group

Working with Scalar and Vector quantities

If you multiply two scalar quantities, is the product still a scalar?
If you multiply a scalar and a vector quantity, what is the product?
If you multiply two vector quantities, what is the product?
And what happens when you divide a scalar by a scalar/scalar by a vector/vector by a scalar/ vector by a vector?
A) yes it's still a scalar
B and C) the product is a vector
not sure about your last question tho, sorry
Original post by hi_imcatherine
If you multiply two scalar quantities, is the product still a scalar?
If you multiply a scalar and a vector quantity, what is the product?
If you multiply two vector quantities, what is the product?
And what happens when you divide a scalar by a scalar/scalar by a vector/vector by a scalar/ vector by a vector?


If you multiply two scalar quantities, is the product still a scalar?

Scalar
Example: density × volume = mass

If you multiply a scalar and a vector quantity, what is the product?

Vector
Example: mass × acceleration = (net) force

If you multiply two vector quantities, what is the product?

It depends. There are 2 “multiplication” operations for vectors: dot product and cross product.

Example: Work done = Force × Displacement in the direction parallel to the force.
This is the dot product of 2 vector quantities which gives a scalar quantity.

Example: Torque = “lever arm vector” × Force
This is the cross product of 2 vector quantities which gives a vector quantity.
https://en.wikipedia.org/wiki/Torque



There is no division operation in vector.
So there is no answer to an ill-posed question. :smile:



But it does show that you are thinking. Keep it up.
Original post by Eimmanuel
Scalar
Example: density × volume = mass


Vector
Example: mass × acceleration = (net) force


It depends. There are 2 “multiplication” operations for vectors: dot product and cross product.

Example: Work done = Force × Displacement in the direction parallel to the force.
This is the dot product of 2 vector quantities which gives a scalar quantity.

Example: Torque = “lever arm vector” × Force
This is the cross product of 2 vector quantities which gives a vector quantity.
https://en.wikipedia.org/wiki/Torque



There is no division operation in vector.
So there is no answer to an ill-posed question. :smile:



But it does show that you are thinking. Keep it up.

Thank you this was really helpful. Why are you unable to divide vectors? Is it true then, that a scalar divided by a scalar is a scalar?
Original post by hi_imcatherine
Why are you unable to divide vectors?


There is no operation of division in dealing with vectors. I know it is a bit hand waving or circular reasoning. I don’t really understand the reason. This is a question for mathematicians (IMO). You can search online.

https://math.stackexchange.com/questions/246594/what-is-vector-division

[QUOTE="hi_imcatherine;83056402"] Is it true then, that a scalar divided by a scalar is a scalar?

Yes.

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