The magnitudes of pairs of displacement vecto | vedclass

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(C) The resultant $R$ of two vectors with magnitudes $A$ and $B$ must satisfy the inequality $|A - B| \leq R \leq A + B$.For a resultant $R = 13 \, cm

Vedclass · Accepted Answer

$1 \, cm, 15 \, cm$

Vedclass · Answer

(C) The resultant $R$ of two vectors with magnitudes $A$ and $B$ must satisfy the inequality $|A - B| \leq R \leq A + B$.For a resultant $R = 13 \, cm$ to be possible,the given magnitudes must satisfy $|A - B| \leq 13 \leq A + B$.Checking the options:$A) \, |4 - 16| = 12$ and $4 + 16 = 20$. Since $12 \leq 13 \leq 20$,this is possible.$B) \, |20 - 7| = 13$ and $20 + 7 = 27$. Since $13 \leq 13 \leq 27$,this is possible.$C) \, |1 - 15| = 14$ and $1 + 15 = 16$. Since $14 \leq 13 \leq 16$ is false,this is not possible.$D) \, |6 - 8| = 2$ and $6 + 8 = 14$. Since $2 \leq 13 \leq 14$,this is possible.Therefore,the pair that cannot produce a resultant of $13 \, cm$ is $1 \, cm$ and $15 \, cm$.

The magnitudes of pairs of displacement vectors are given. Which pair of displacement vectors cannot be added to give a resultant vector of magnitude $13 \, cm$?

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