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Two vectors \(A\) and \(B\) lie in a plane. Another vector \(C\) lies outside this plane. The resultant \(A + B + C\) of these three vectors

1. can be zero
2. cannot be zero
3. lies in the plane of \(A\) and \(B\)
4. lies in the plane of \(A\) and \(A + B\)

Correct answer: cannot be zero

Solution

The sum \(A+B\) lies in the plane of \(A\) and \(B\). Since \(C\) has a component perpendicular to this plane, that component cannot be cancelled by \(A+B\). Therefore the total resultant cannot be zero.

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