Given that \(r = 2i - j\), \(s = 3i + 5j\) and \(t = 6i - 2j\), find the magnitude of \(2r + s - t\).
Answer Details
We are given that:
\begin{align*}
r &= 2i - j\\
s &= 3i + 5j\\
t &= 6i - 2j
\end{align*}
We can now substitute these expressions into \(2r+s-t\) and simplify:
\begin{align*}
2r + s - t &= 2(2i-j) + (3i+5j) - (6i - 2j)\\
&= 4i - 2j + 3i + 5j - 6i + 2j\\
&= i + 5j
\end{align*}
The magnitude of a vector with components \(a\) and \(b\) is given by \(\sqrt{a^2 + b^2}\). So, the magnitude of \(i+5j\) is:
\begin{align*}
\sqrt{i^2 + 5j^2} &= \sqrt{1^2 + 5^2} \\
&= \sqrt{26}
\end{align*}
Therefore, the answer is \(\sqrt{26}\).