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(B) Let the vectors be $\vec{A}, \vec{B}, \vec{C}, \dots$ with $x$-components $A_x, B_x, C_x, \dots$ and magnitudes $A, B, C, \dots$.The resultant vec

Vedclass · Accepted Answer

$(a), (b), (c)$

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(B) Let the vectors be $\vec{A}, \vec{B}, \vec{C}, \dots$ with $x$-components $A_x, B_x, C_x, \dots$ and magnitudes $A, B, C, \dots$.The resultant vector is $\vec{R} = \vec{A} + \vec{B} + \vec{C} + \dots$.The $x$-component of the resultant is $R_x = A_x + B_x + C_x + \dots$.Thus,statement $(a)$ is correct.Since the $x$-component of any vector is always less than or equal to its magnitude $(A_x \le A)$,the sum of $x$-components is $R_x = \sum A_x \le \sum A$.This means $R_x$ is always less than or equal to the sum of the magnitudes of the vectors.Therefore,$R_x$ can be less than the sum of magnitudes (statement $(b)$ is correct).However,$R_x$ cannot be greater than the sum of magnitudes,so statement $(c)$ is incorrect.$R_x$ is not necessarily equal to the sum of magnitudes (statement $(d)$ is incorrect).Thus,statements $(a)$ and $(b)$ are correct.

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

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