Help with Vector Multiplication please

[Martyn Arthur]

Homework Statement

Produce an outcome to given equation

Relevant Equations

((sinpsii)+(cospsij))*(xzi+yj+(x+y)k

Hi I am not looking for the calculation to be done; thats my job. I can't figure out the format of the multiplication.
Is it ((sinpsii)(xzi)+(cospsij))(xzi)+((sinpsii)yj+(cospsij))yj +((sinpsii)(x+y)k+(cospsij))(x+y)k then requiring simplification?
Thanks
Martyn

 

[D H]

Homework Statement: Produce an outcome to given equation
Relevant Equations: ((sinpsii)+(cospsij))*(xzi+yj+(x+y)k

Your relevant equation is ill-formed; it is missing a right parenthesis. I would presume the missing right parenthesis could go after the xzi+yj term, or at the very end. That makes it a bit hard to tell.

 

[pasmith]

Is * the dot product or the cross product? In either case, they are distributive over vector addition.

 

[Mark44]

Homework Statement: Produce an outcome to given equation
Relevant Equations: ((sinpsii)+(cospsij))*(xzi+yj+(x+y)k

First off, that's not an equation -- an equation states the equality (using an = sign) of two or more expressions.
Second, that's very difficult to read. Using the form of LaTeX that we have here at PF, the expression becomes one or the other or the following:
$(\sin(\psi)\hat i + \cos(\psi)\hat j) \cdot (xz\hat i +y\hat j + (x + y)\hat k)$ (dot product) or
$(\sin(\psi)\hat i + \cos(\psi)\hat j) \times (xz\hat i +y\hat j + (x + y)\hat k)$ (cross product)

Third, as already noted, we don't know (do you?) which kind of multiplication is to be performed, whether it's the scalar product (AKA dot product) or vector product (AKA cross product). They are very different, with one difference being that the result of the first is a scalar -- a number, and the result of the second being a vector.

 

[Martyn Arthur]

Thanks for the responses, points noted, missing bracket follows at the end af the statement. I am working on the basis of the procedure I have been given attached.

 

[Steve4Physics]

@Martyn Arthur - Su’mae (but that’s my limit!).

Is it ((sinpsii)(xzi)+(cospsij))(xzi)+((sinpsii)yj+(cospsij))yj +((sinpsii)(x+y)k+(cospsij))(x+y)k then requiring simplification

That depends on what the original question was - which you haven't told us.

Thanks for the responses, points noted, missing bracket follows at the end af the statement. I am working on the basis of the procedure I have been given attached. View attachment 355455

It's not clear how the 'procedure' relates to the original question (though we could guess).

And you haven’t yet clearly answered what you were asked in previous posts: do you want the scalar (dot) product or the vector (cross) product?

 

[vela]

I can't figure out the format of the multiplication.

I don't understand what you mean by "format of the multiplication."

Is it ((sinpsii)(xzi)+(cospsij))(xzi)+((sinpsii)yj+(cospsij))yj +((sinpsii)(x+y)k+(cospsij))(x+y)k then requiring simplification?

It seems like you're asking if
$$\vec A \cdot (B_x\,\hat i + B_y\,\hat j + B_z\,\hat k) = \vec A \cdot (B_x\,\hat i) + \vec A \cdot (B_y\,\hat j) + \vec A \cdot (B_z\,\hat k)$$ is true where $\cdot$ denotes the scalar or dot product. The answer, as @pasmith noted above, is yes.

That said, I'm going to suggest you first review how to calculate the dot product of two vectors given their cartesian component representation. That is, if $\vec A = A_x\,\hat i + A_y\,\hat j + A_z\,\hat k$ and $\vec B = B_x\,\hat i + B_y\,\hat j + B_z\,\hat k$, what is $\vec A \cdot \vec B$ equal to in terms of the components? It'll make calculations like the one you're looking at easier to do.