Yes.
Two vectors, no; three vectors yes.
Two - if you add two vectors of equal magnitude but in opposite directions, the resultant vector is zero.
Yes, put the three vectors in a plane, with a separation of 120 degrees between each vector and each of the other vectors.
The only way that two vectors add up to zero is if they have equal magnitude and opposite direction. If the magnitudes are not equal then no, they cannot give a zero resultant.
Yes.
Two vectors, no; three vectors yes.
Two - if you add two vectors of equal magnitude but in opposite directions, the resultant vector is zero.
a resultant vector
Yes, put the three vectors in a plane, with a separation of 120 degrees between each vector and each of the other vectors.
The only way that two vectors add up to zero is if they have equal magnitude and opposite direction. If the magnitudes are not equal then no, they cannot give a zero resultant.
Yes.
Sum of two vectors can only be zero if they are equal in magnitude and opposite in direction. So no two vector of unequal magnitude cannot be added to give null vector. Three vectors of equal magnitude and making an angle 120 degrees with each other gives a zero resultant.
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.
at 120 degree
No. For three vectors they must all lie in the same plane. Consider 2 vectors first. For them to resolve to zero, they must be in opposite direction and equal magnitude. So they will lie along the same line. For 3 vectors: take two of them. Any two vectors will lie in the same plane, and their resultant vector will also lie in that plane. Find the resultant of the first two vectors, and the third vector must be along the same line (equal magnitude, opposite direction), in order to result to zero. Since the third vector is along the same line as the resultant vector of the first two, then it must be in the same plane as the resultant of the first two. Therefore it lies in the same plane as the first two.
Two vectors: no. Three vectors: yes.
In vector addition, the sum of two (or more) vectors will give a resultant vector. There are a number of sites that will help you with tutorials. A link to one can be found below.