find a unit vector perpendicular to both (2,1,1) and the x-axis?

Question

I can find a vector perpendicular to (2,1,1) but what does it mean by perpendicular to x axis?

Answer 1

(2,1,1) x (1, 0, 0) = (0, 1, -1)
Change to a unit vector: (0, 1/√2, -1/√2)
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Ideas to save time: Use cross product.

Answer 2

x axis is represented by a vector (1, 0 ,0)

hint:
use cross product of 3 vectors
(1,0,0)
(2,1,1) and
(x, y,z) to be determined (using perpendicularity)

Answer 3

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Answer 4

call it (a,b,c) with a^2+b^2+c^2=1
2a+b+c=0 Dot product with the given vector
Dot product with (1,0,0) = a=0
so
b+c=0
and b^2+c^2=1 so 2b^2=1 and b= +-1/2 sqrt(2)
one solution is (0,1/2 sqrt(2),-1/2 sqrt(2) )
The other changing signs