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We're not sure what you have in mind when you say "counteract". But two vectors
can certainly add up to zero, if their magnitudes are equal and their directions are
different by exactly 180 degrees. In that case, they have the same effect as if they
were both not there at all.
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What is the condition when two vectors are addition and subtraction are same magnitude?
The condition is the two vectors are perpendicular to each other.
What is the angle needed for the smallest resultant of two vectors?
The smallest resultant of two vectors is the sum of two equal vectors which make an angle of 180 degrees among each other.
Can any vector be represented by two other vectors that are right angels to each others?
Yes. This is the basis of cartesian vector notation. With cartesian coordinates, vectors in 2D are represented by two vectors, those in 3D are represented by three. Vectors are generally represented by three vectors, but even if the vector was not in an axial plane, it would be possible to represent the vector as the sum of two vectors at right angles to eachother.
Which are those two vectors whose resultant vector is zero?
They are vectors of equal magnitudes in oppositedirections. When you add them, they cancel out each other.
Can two nonzero vectors give zero resultant when they multiply with each other if yes give condition for same?
yes, if they are at right angles to each other.
