The x-component of the resultant of several v | vedclass

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(B) Let there be $n$ vectors $\vec{A}_1, \vec{A}_2, ..., \vec{A}_n$ with $x$-components $A_{1x}, A_{2x}, ..., A_{nx}$ and magnitudes $|\vec{A}_1|, |\v

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$(b)$ may be smaller than the sum of the magnitudes of the vectors.

Vedclass · Answer

(B) Let there be $n$ vectors $\vec{A}_1, \vec{A}_2, ..., \vec{A}_n$ with $x$-components $A_{1x}, A_{2x}, ..., A_{nx}$ and magnitudes $|\vec{A}_1|, |\vec{A}_2|, ..., |\vec{A}_n|$.The resultant vector is $\vec{R} = \sum_{i=1}^{n} \vec{A}_i$.The $x$-component of the resultant is $R_x = \sum_{i=1}^{n} A_{ix}$. Thus,statement $(a)$ is correct.Since $|A_{ix}| \le |\vec{A}_i|$,the sum of $x$-components $\sum A_{ix} \le \sum |\vec{A}_i|$. Therefore,the $x$-component of the resultant is generally smaller than or equal to the sum of the magnitudes of the vectors. Thus,statement $(b)$ is correct.Statement $(c)$ is incorrect because the $x$-component of a vector cannot exceed its own magnitude,and consequently,the sum of $x$-components cannot exceed the sum of magnitudes.Statement $(d)$ is only true if all vectors are directed along the positive $x$-axis. In general,it is not true. Thus,statement $(d)$ is incorrect.Therefore,the correct statements are $(a)$ and $(b)$.

The $x$-component of the resultant of several vectors is:

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