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

[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.

 

[Integral]

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

 

[mr_coffee]

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

 

[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)

 

[mr_coffee]

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

 

[TD]

You're welcome