what is the min number of non--parallel vectors are needed in a plane (2D vector space) to give zero resultant vector? (ie. all add and give zero vector)
Answers
In any space of one dimension or more, the minimum number of nonzero vectors that can be added to givea zero resultant is two. The two vectors would have equal magnitude and opposite direction. If collinearvectors are not allowed then the minimum is three for any space of two dimensions or more.
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Answer:
Statement 1 is true because:
2 vectors to have resultant zero means,
(a i
^ +
bj
^)+
(c i
^ +
dj
^)=
0
or,
c=
−a,d=
−b
.
Thus 2 vectors need to be equal in magnitude and opposite in direction. But for 3, we can have unequal vectors, like
5 i
^ ,−3 i
^ ,−2 i
^
Statement 2 is also correct because if they are not coplanar, then one vector would have a component in the plane perpendicular to the other two, which would mean that sum can't be zero.
Thus both statements are correct but statement 2 doesn't explain statement 1