# scalar product and vector product combined

• Mar 30th 2012, 02:13 AM
Stuck Man
scalar product and vector product combined
I believe there is a typo in this sentence from a book. Can someeone confirm it?

"Since a.b is a scaler then (a.b)xc has no meaning and a.(bxc) may be wriiten as a.bxc without ambiguity."
• Mar 30th 2012, 02:36 AM
Plato
Re: scalar product and vector product combined
Quote:

Originally Posted by Stuck Man
I believe there is a typo in this sentence from a book. Can someeone confirm it?
"Since a.b is a scaler then (a.b)xc has no meaning and a.(bxc) may be wriiten as a.bxc without ambiguity."

What do you think is a typo?
I may not care for the way it is written, but I see no typo.
It says: because $\displaystyle (A\cdot B)\times C$ has no meaning we can write $\displaystyle A\cdot B\times C$ and understand it as $\displaystyle A\cdot(B\times C).$
• Mar 30th 2012, 02:58 AM
Stuck Man
Re: scalar product and vector product combined
Why do the brackets say nothing? I find it extremely unusual that brackets are not observed. This is not what I find with a Casio calculator.
• Mar 30th 2012, 03:09 AM
Plato
Re: scalar product and vector product combined
Quote:

Originally Posted by Stuck Man
Why do the brackets say nothing? I find it extremely unusual that brackets are not observed. This is not what I find with a Casio calculator.

I have no idea what "Why do the brackets say nothing?" could mean.
These are vectors. $\displaystyle A\cdot B$ is a scalar, a number.
Cross products are vectors. If $\displaystyle t$ is a scalar and $\displaystyle C$ is a vector then $\displaystyle t\times C$ is meaningless.
A calculator has absolutely nothing to do with vectors.
• Mar 30th 2012, 03:21 AM
Stuck Man
Re: scalar product and vector product combined
I thought that t x C was multiplying the vector C by a scaler. It is not the same as tC then? My fx-991 does have a vector mode. I'm not sure now if it does vector products.
• Mar 30th 2012, 03:29 AM
Stuck Man
Re: scalar product and vector product combined
My calculator does not follow what is being said in that quote from the book. It can do vector products with AxB or AB or A(B).
• Mar 30th 2012, 03:42 AM
Plato
Re: scalar product and vector product combined
Quote:

Originally Posted by Stuck Man
My calculator does not follow what is being said in that quote from the book. It can do vector products with AxB or AB or A(B).

If $\displaystyle A=<1,2,3>~\&~B=<2,3,1>$ then $\displaystyle A\times B=<-7,5,-1>$.
If your calculator does not give that answer, then put it in a drawer and forget it.
• Mar 30th 2012, 08:09 AM
HallsofIvy
Re: scalar product and vector product combined
Quote:

Originally Posted by Stuck Man
I thought that t x C was multiplying the vector C by a scaler. It is not the same as tC then? My fx-991 does have a vector mode. I'm not sure now if it does vector products.

No, the product of scalar t and vector C is denoted by tC. The "x" is reserved for the cross product.
• Mar 30th 2012, 08:11 AM
HallsofIvy
Re: scalar product and vector product combined
Quote:

Originally Posted by Stuck Man
My calculator does not follow what is being said in that quote from the book. It can do vector products with AxB or AB or A(B).

Taking Plato's example of A= <1, 2, 3> and B= <3, 2, 1>, what does your calculator give for AB or A(B)? There are two kinds of "vector times vector" product (well, three if you include the "exterior product- the exterior product of two n dimension vectors is a n by n tensor.) so the notation "AB" or A(B) is ambiguous.
• Mar 30th 2012, 10:32 AM
Stuck Man
Re: scalar product and vector product combined
I get the vector product, -4i, 8j, -4k for AB, A(B) and AxB with the calculator.

I have noticed that with the calculator the scaler product has higher precedence than the vector product which has been confusing me. The vector product has precedence in mathematics. I feel that Casio should fix this with later models.
• Mar 30th 2012, 11:11 AM
Plato
Re: scalar product and vector product combined
Quote:

Originally Posted by Stuck Man
I get the vector product, -4i, 8j, -4k for AB, A(B) and AxB with the calculator.
I have noticed that with the calculator the scaler product has higher precedence than the vector product which has been confusing me. The vector product has precedence in mathematics. I feel that Casio should fix this with later models.

You are not using that calculator correctly.
Look at this web page.

Look at the dot product.
• Mar 30th 2012, 11:32 AM
Stuck Man
Re: scalar product and vector product combined
I am. HallsOfIvy copied B wrongly and I used it. I am still questioning why the calculator puts the dot product above the vector product.
• Mar 30th 2012, 01:17 PM
HallsofIvy
Re: scalar product and vector product combined
Once again, if you do the dot product first, you do NOT have two vectors and cannot do the cross product.