Question

Given the vectors U=(2,1,-4) and V=(3,1,2) Find all the vectors which are perpendicular on U and V using:

a) The dot product
b) The cross product

Answer 1

1) For dot product there is a system. X is a vector we need to find:
\(\overrightarrow u \cdot \overrightarrow x=0\)
\(\overrightarrow v\cdot \overrightarrow x=0\)
Here you have 2 equations and 3 variables (components of X).
2) Every vector that is perpendicular on any two vectors has the same direction as the cross product of these two vectors. So:
\(\overrightarrow x=\alpha (\overrightarrow u\times\overrightarrow v) \)

Answer 2

All you have to know to solve your problem is to know formulas for dot and cross products and read above.

Answer 3

\[\rm \langle a_1,a_2\cdots\rangle \mathbf{\Large \cdot }\langle b_1, b_2\cdots\rangle = a_1b_1+a_2b_2\cdots\]

Answer 4

Ok so for the dot product I will get a parametric equation?

Answer 5

And a cartesian equation for the cross product right?

Answer 6

Yes. If your vectors are in the cartesian coordinate system.

Answer 7

Alright, thank you very much. I just want to say that you guys and this site are awesome. Honestly I really didn't expect an answer this fast. Thank you very much.