Question

At what angle should the two force vectors 5 N and 12 N added to get a resultant vector of 13 N .​

Answer 1

$\large{\bf{\underline{Required~Answer:-}}}$

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$\begin{lgathered}\frak{Given}\begin{cases}\sf{Two~force~vectors~are~=5~N~and~12~N}\\\sf{Resultant~vector~is~=13~N}\end{cases}\end{lgathered}$

To find:- Find the angle

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Solution:-

Let two vectors are A and B

So,

• A vector = 5 N

• B vector = 12 N

• R vector = 13 N

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Here,

${\sf{:\implies R = A + B}}$

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${\sf{:\implies R.R = (A + B).(A + B)}}$

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${\sf{:\implies R^{2}=A^{2} + B^{2}+2AB.\:cos \theta...(Where\: \theta\:be\:the\:angle\:between\:the\:vectors\:A\:and\:B)}}$

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${\sf When\: R\:=\:13\:N}$

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Now,

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${\sf{:\implies (13)^{2} = (5)^{2} + (12)^{2} + 2×5×12\:cos \theta}}$

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${\sf{:\implies cos \theta = 0}}$

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${\sf{:\implies cos \theta = 90°}}$

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$\begin{lgathered}\\:\implies\:\underline{\boxed{\bf{\purple{ \theta=90°}}}}\:\bigstar\end{lgathered}$

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$\therefore\:{\underline{\sf{Hence,\: The\:angle\: between\: the\: two\: force\: vectors\:is\: 90°}}}$

Answer 2

Answer:

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