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.
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You get other vectors, usually perpendicular to each other, that - when added together - result in the original vector. These component vectors are usually along the axes of some selected coordinate system.
Vectors are added by head to tail rule.
Yes, put the three vectors in a plane, with a separation of 120 degrees between each vector and each of the other vectors.
The condition is the two vectors are perpendicular to each other.
Forces have to be added as vectors. This means that in certain cases, the forces can cancel, and in other cases they can be added.