Question

Is the dot product: vector (dot) vector= scalar?
cross product = vector (dot) vector = vector?

Answer 1

yes

Answer 2

well, the dot in cross should be an x

Answer 3

cross product is for both 2-d and 3-d?

Answer 4

@amistre64 oh yes,

Answer 5

\[dot:\vec u \cdot \vec v=n\]\[cross:\vec u \times \vec v=\vec s\]

Answer 6

thanks

Answer 7

youre welcome

Answer 8

can dot product be scalar (dot) scalar?
or scalar(dot) vector?

Answer 9

the operations are defined on vectors ... you can relate it to a linear vector space (1 0) if need be

Answer 10

hmmm, by applying the definition of a dot product we can produce the elements needed for the resultant vector

\[\binom{1}{0}(-3)=\binom{-3\cdot 1}{-3\cdot 0}=\binom{-3}{0}\]

but the operations are not defined particularly for non vector spaces

Answer 11

an R^1 vectors looks like a number, yes but it has to be viewed in the context of its 1-dimentional vector space

Answer 12

\[\vec u=(3)~:~\vec v=(-4)\]
\[\vec u\cdot \vec v = 3(-4)=-12\]
\[\vec u\times \vec v = 0\]

Answer 13

how did it become zero?

Answer 14

\[det\begin{pmatrix}3&-4\\0&0\end{pmatrix}=3(0)+4(0)=0\]

Answer 15

or rather \[\vec 0\]

Answer 16

oh..I see thanks

Answer 17

another way to consider it is that in R^1, vectors either in the same direction, or 180 degrees opposites

in either case, they are scalar multiples of each other and have a zero determinant in the cross

Answer 18

take R^2 examples:

http://www.wolframalpha.com/input/?i=%5B1%2C2%5D+x+%5B-1%2C-2%5D

http://www.wolframalpha.com/input/?i=%5B1%2C2%5D+x+%5B2%2C4%5D

Answer 19

thank you...

Answer 20

youre welcome