dot product

[rinspd]

Suppose a and b are vectors which lie in the plane 3x+2y-5z = 1.
Find (2a + 3b) · <3, 2, -5> .
is it equal to 0?

 

[Deleted member 4993]

Suppose a and b are vectors which lie in the plane 3x+2y-5z = 1.
Find (2a + 3b) · <3, 2, -5> .
is it equal to 0?

Yes .... but why?

What does <3,2,-5> mean to you?

 

[pka]

Suppose a and b are vectors which lie in the plane 3x+2y-5z = 1.
Find (2a + 3b) · <3, 2, -5> .
is it equal to 0?

I have real quibble with the wording of this question.
It is used incorrectly by many authors.
Vectors are equivalence classes and as such do not belong to any particular plane.

It should read "Suppose a and b are vectors which are parallel the plane 3x+2y-5z = 1." Therefore, they are perpendicular to the plane's normal.