Working with Scalar and Vector quantities

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hi_imcatherine
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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?
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LaurenRosie
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A) yes it's still a scalar
B and C) the product is a vector
not sure about your last question tho, sorry
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Eimmanuel
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(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.



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



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?
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Eimmanuel
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(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/quest...ector-division

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

Yes.
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