Which one of the following pairs cannot be th | vedclass

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(D) For a vector of magnitude $F = 10 \, N$ to have rectangular components $F_x$ and $F_y$,it must satisfy the condition $F = \sqrt{F_x^2 + F_y^2}$,wh

Vedclass · Accepted Answer

$9 \, N$ and $1 \, N$

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(D) For a vector of magnitude $F = 10 \, N$ to have rectangular components $F_x$ and $F_y$,it must satisfy the condition $F = \sqrt{F_x^2 + F_y^2}$,which implies $F^2 = F_x^2 + F_y^2 = 10^2 = 100$.Checking each option:$A$: $6^2 + 8^2 = 36 + 64 = 100$. (Possible)$B$: $7^2 + (\sqrt{51})^2 = 49 + 51 = 100$. (Possible)$C$: $(6\sqrt{2})^2 + (2\sqrt{7})^2 = (36 	imes 2) + (4 	imes 7) = 72 + 28 = 100$. (Possible)$D$: $9^2 + 1^2 = 81 + 1 = 82 
eq 100$. (Not possible)Therefore,the pair $9 \, N$ and $1 \, N$ cannot be the rectangular components.

Which one of the following pairs cannot be the rectangular components of a force vector of $10 \, N$?

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