Homework Help: Dot product, i don't see what they want from me

1. Sep 22, 2005

mr_coffee

hello everyone, i understand the dot product and its properties but i don't get what they want! They say....
The dot product of two vectors are perpendicular if a.b = 0.
Then any vector in R^3 perpendicular to

-5
-6
-3

note: that is a matrix above.

can be written in the form:
and it looks like parameteric forum they want, because they want a column of s and a column of t. but i don't see where i'm suppose to find more numbers.

2. Sep 22, 2005

Integral

Staff Emeritus
Call the vector you are given A, you need to find, and descripe the family of vectors (b) which satisfy the condition:

$$A \cdot b = 0$$

3. Sep 22, 2005

mr_coffee

thanks for the responce!
how do you find a family of vectors?

4. Sep 23, 2005

TD

First, take anoter "general" vectors, let's say (x,y,z). Take the dot product with (-5,-6,-3) and let it equal 0.
Now you have 1 equation with 3 variables which has infinite many solutions. Solve it by choosing two variables (e.g. let x = s and y = t, then solve for z)

5. Sep 23, 2005

mr_coffee

Awesome! thanks again TD, you should be getting paid for this hah. :tongue:

6. Sep 23, 2005

TD

You're welcome
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