Question
Given a + b + c + d = 0, which of the following statements are correct:b + c must lie in the plane of a and d if a and d are not collinear, and in the line of a and d, if they are collinear?

Answer

Correct.Explanation:
a + b + c + d = 0, a + (b + c) + d = 0, The resultant sum of the three vectors a, (b + c), and d can be zero only if (b + c) lie in a plane containing a and d, assuming that these three vectors are represented by the three sides of a triangle. If a and d are collinear, then it implies that the vector (b + c) is in the line of a and d. This implication holds only then the vector sum of all the vectors will be zero.

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