Two forces \(F_{1} = (7i + 8j)N\) and \(F_{2} = (3i + 4j)N\) act on a particle. Find the magnitude and direction of \(F_{1} - F_{2}\).
Question 1 Report
Two forces \(F_{1} = (7i + 8j)N\) and \(F_{2} = (3i + 4j)N\) act on a particle. Find the magnitude and direction of \(F_{1} - F_{2}\).
Answer Details
To find the magnitude and direction of \(F_{1} - F_{2}\), we need to subtract the components of \(F_{2}\) from \(F_{1}\).
\begin{align*}
F_{1} - F_{2} &= (7i + 8j) - (3i + 4j)\\
&= 4i + 4j\\
\end{align*}
The magnitude of \(F_{1} - F_{2}\) is given by:
\begin{align*}
|F_{1} - F_{2}| &= \sqrt{(4)^2 + (4)^2}\\
&= 4\sqrt{2} N\\
\end{align*}
The direction of \(F_{1} - F_{2}\) is given by:
\begin{align*}
\theta &= \tan^{-1}\left(\frac{4j}{4i}\right)\\
&= \tan^{-1}(1)\\
&= 45°\\
\end{align*}
Therefore, the magnitude and direction of \(F_{1} - F_{2}\) are \((4\sqrt{2} N, 045°)\). Answer is correct.
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