YES
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Consider an equilateral triangle. If each vector started at the center of the triangle and went through a different vertex than the other two vectors then they would cancel. I believe in order for them to add to a null vector they must be co-planer.
No. The vector resultant of addition of vectors is the vector that would connect the tail of the first vector to the head of the last. For any set of vectors to add to the zero vector, the endpoint of the last vector added must be coincident with the start point of the first. Therefore for the sum of only two vectors to have a chance of being the zero vector, the second vector must be in a direction exactly opposite the first. So you can tell that the result of adding the two vectors could only can be zero vector if the two vectors were of two equal magnitude.
You get a third vector.
Yes, two vectors of similar kind can be added. For example we can add a distance vector with another distance vector. But we cannot add distance vector and velocity vector.
The sum of two null vectors is a null vector. And since a direction is not relevant for a null vector, the resultant has no direction either.