I can't visualize it!
Level
1
Are the vectors <1,1,1> and <1,1,-1> perpendicular?
Yes
No
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To hep you visualize this :) . These vectors have x and y components same but opposite z. So its like having a mirror on the x,y plane and they exist on a vertical plane. To check geometricaly if they are perpendicular is better to see their image on that vertical plane where it is easy to see.