what would 2 orthogonal vectors in the plane x+y+2z=0 be.?

Answer 1

To solve this remember:

The dot product of orthogonal (normal) vectors is zero.
The cross product of two vectors is a vector that is normal to both of them.

The normal vector to the plane is <1,1,2>
Any vector in the plane will be normal to this vector.
Let's choose one: <1,-1,0>
Checking for orthogonality: <1,1,2>.<1,-1,0> = 0

Now take the cross product of these two vectors:
<1,1,2> X <1,-1,0> = <2,2,-2>

Checking for orthogonality: <1,1,2>.<2,2,-2> = 0

Checking for orthogonality: <1,-1,0>.<2,2,-2> = 0

So two orthogonal vectors in the plane are:
<1,1,0>
<2,2,-2>

Answer 2

[1 1 -2]
[1 -1 0]

Answer 3

my graphing cacl. is in my car, sorry, but i am an engineering major, so if you want to email me with Q's go for it