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tonykart44
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
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: \(\overrightarrow x=\alpha (\overrightarrow u\times\overrightarrow v) \)
All you have to know to solve your problem is to know formulas for dot and cross products and read above.
\[\rm \langle a_1,a_2\cdots\rangle \mathbf{\Large \cdot }\langle b_1, b_2\cdots\rangle = a_1b_1+a_2b_2\cdots\]
Ok so for the dot product I will get a parametric equation?
And a cartesian equation for the cross product right?
Yes. If your vectors are in the cartesian coordinate system.
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.