Multiple Choice

The x-component of the resultant of several vectors

Ais equal to the sum of the x-components of the vectors
Correct Answer
Bmay be smaller than the sum of the magnitudes of the vectors
Correct Answer
Cmay be greater than the sum of the magnitudes of the vectors
Dmay be equal to the sum of the magnitudes of the vectors.
Correct Answer

Solution

The sum of x-component of the resultant of several vectors is either smaller than or equal to the magnitude of all the vectors.

This is because when we separate the vector into its resultant the magnitude of the resultant vector decreases , and various factors such as +x and -x directions even cancel a huge amount of magnitude which brings it to a smaller magnitude.

But if we consider vectors which are all parallel and in +x direction, the x-component is the vector itself and the magnitude of sum of all vectors is equal to sum of x-components.
hence,
option A,B and D are correct.

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