Understanding Vector Products - Mike's Query

[mikedamike]

Hi,

i was wondering if anyone could confirm what a vector product is.

|1| |4| |1x4|
|2| X |5| = |2x5|
|3| |6| |3x6|

Im presuming a vector product by multiplying the corresponding elements?

I have problem where i have to 3x1 vectors and i have to find the vector product.

Thanks in advance
Regards
Mike

 

[Rasalhague]

No, it's not simply componentwise multiplication. Vector product is synonymous with (=means the same thing as) cross product. Google either name for definitions. There are two equivalent definitions. One involves a matrix determinant formula, the other expresses the cross product in terms of the sine of the angle between the vectors.

 

[HallsofIvy]

Do you mean the dot product of <1, 2, 3>.<4, 5, 6>? If so no, that is not correct. The dot product of two vectors is a NUMBER, not a vector. <1, 2 3>.<4, 5 6>=1(4)+ 2(5)+ 3(6)= 4+ 10+ 16= 30.

I used the term, "dot product" rather than "vector product" because there are several different products involving vectors- the "scalar product" of a number, x, with a vector, <u, v, w> is the vector, <xu, xv, xw>. The "dot product", which I used above, of a vector <a, b, c> with a vector <u, v, w> is the number au+ bv+ cw. The "cross product (using "x" rather than ".") of a vector <a, b, c> with a vector <u, v, w> is the vector <bw- cv, cu- aw, av- bu>.