Question

Hello
What is the difference between a dot product and a cross product and how do i find a vector parallel to (2,-3,6)

Answer 1

Dot products and cross products are very different. Look at the result: one gives a scalar, the other gives another vector.

Answer 2

...and multiplying a vector by any positive scalar will not change it's direction

Answer 3

The dot product is computed as follows: \[
\left[\begin{matrix}
a_1\\a_2\\a_3
\end{matrix}\right]\cdot\left[\begin{matrix}
b_1\\b_2\\b_3
\end{matrix}\right]=a_1b_1+a_2b_2+a_3b_3
\]The pattern remains the same for larger vectors.

Answer 4

\[a= \left(\begin{matrix}a_1 \\ a_2 \\ a_3\end{matrix}\right) \text{ , } b =\left(\begin{matrix}b_1 \\ b_2 \\ b_3\end{matrix}\right)\]
\[a . b = |a||b|\cos \theta = a_1b_1 + a_2b_2 + a_3b_3\]

Answer 5

The cross product can be computed as the determinant of the following matrix:\[
\left|\begin{matrix}
i&j&k\\a_1&a_2&a_3\\b_1&b_2&b_3
\end{matrix}\right|
\]

Answer 6

\[a \times b = \det\left[\begin{matrix}i & j & k \\ a_1 & a_2 & a_3 \\ b_1 & b_2 & b_3\end{matrix}\right]\]

Answer 7

damnit you're too quick! XD

Answer 8

Hahaha XD

Answer 9

ok I'm slow with latex...

Answer 10

haha

Answer 11

\[\left|\begin{matrix}
\hat i&\hat j&\hat k\\a_1&a_2&a_3\\b_1&b_2&b_3
\end{matrix}\right|\]I added the hats :)

Answer 12

Nice. Alternatively, boldface!\[
\left|\begin{matrix}
\mathbf{i}&\mathbf{j}&\mathbf{k}\\a_1&a_2&a_3\\b_1&b_2&b_3
\end{matrix}\right|
\]

Answer 13

\mathbf
news to me, thanks

Answer 14

thanks bouscal and turning and eigen