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CBSE Class 11-science Answered

Minimum number of non-coplanar vectors whose sum can be zero is four. Why?
Asked by bidrohiSP57 | 29 Sep, 2018, 08:33: AM
answered-by-expert Expert Answer
Two vectors are alwys coplanar. Let us add a third vector to make all the three vectors coplanar.
The third vector canbe resolved so that one copmonent is in the plane of vectors formed by the first and second vector.
The other component is perpendicular to this plane. Obviously the resulatant can not be zero,
becuase two vectors and the resolved component of third vector are in a plane and other resolved component is perpendicular to that plane.
 
Now we add a fourth vector which is not in the plane formed by first two vectors.
Now let us resolve the fourth vector so that one componet is on the plane formed by the first two vectors
and other component is perpendicular to taht plane. Now we have two initial vectors, resolved components of third
and fourth vector are in a plane. By adjusting their magnitudes we can make the resulatant vector in the plane is zero.
Similarly we have resolved components of third and fourth vector perpendicular to the above mentioned plane.
By adjusting their magnitude it is possible to make the resultant zero.
 
Conclusion:- minimum number of non-coplanar vectors, whose sum is zero, is four
Answered by Thiyagarajan K | 29 Sep, 2018, 03:28: PM
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