Yes. A vector has magnitude and direction. If the vectors have equal magnitude and directly opposite directions their sum will be zero.
Thee direction of the two vectors.
The zero-vector has no direction.
-- A singe vector with a magnitude of zero produces a zero resultant.-- Two vectors with equal magnitudes and opposite directions produce a zero resultant.
No. The tenth vector would have to be matched by one equal and opposite vector to yield a zero resultant, or by multiple vectors in the second plain collectively yielding a zero resultant for that plane. It would be possible, for example, for 8 vectors to be on the same plane and two on a different plane to give a zero resultant.
No.
Two - if you add two vectors of equal magnitude but in opposite directions, the resultant vector is zero.
Thee direction of the two vectors.
The resultant of two vectors is a third vector., for example V1 + V2 = V3. V3 may be equal to zero, greater than zero or less than zero.
The zero-vector has no direction.
If the sum of their components in any two orthogonal directions is zero, the resultant is zero. Alternatively, show that the resultant of any two vectors has the same magnitude but opposite direction to the third.
-- A singe vector with a magnitude of zero produces a zero resultant.-- Two vectors with equal magnitudes and opposite directions produce a zero resultant.
equal and opposite
Assuming you want non-zero vectors, two opposing vectors will give a resultant of zero.
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.
0=v1+v2 means the magnitudes are zero or equal and opposite.
In order for two vectors to add up to zero:-- their directions must be exactly opposite-- their magnitudes must be exactly equal
No. The tenth vector would have to be matched by one equal and opposite vector to yield a zero resultant, or by multiple vectors in the second plain collectively yielding a zero resultant for that plane. It would be possible, for example, for 8 vectors to be on the same plane and two on a different plane to give a zero resultant.