In order for two vectors to add up to zero:
-- their directions must be exactly opposite
-- their magnitudes must be exactly equal
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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.
One-dimensional
If the point's ordinate, or y-coordinate, is zero then it must lie on the x-axis somewhere.
vectors that have same direction and lie on same plane .example a person sitting in an aeroplane or helicopter, a person on a sale boat.
Vector A is parallel to the cross product of vectors B and C, and it is parallel to the axis that neither B or C lie along if the two other axes are defined as the axes that B and C lie along.