If \(p = \begin{pmatrix} 2 \\ -2 \end{pmatrix} \) and \(q = \begin{pmatrix} 3 \\ 4 \end{pmatrix}\), find \(|q - \frac{1}{2}p|\).
Question 1 Report
If \(p = \begin{pmatrix} 2 \\ -2 \end{pmatrix} \) and \(q = \begin{pmatrix} 3 \\ 4 \end{pmatrix}\), find \(|q - \frac{1}{2}p|\).
Answer Details
To find the value of |q - 1/2p|, we first need to calculate q - 1/2p.
q - 1/2p = \(\begin{pmatrix} 3 \\ 4 \end{pmatrix}\) - 1/2\(\begin{pmatrix} 2 \\ -2 \end{pmatrix}\) = \(\begin{pmatrix} 3 \\ 4 \end{pmatrix}\) - \(\begin{pmatrix} 1 \\ -1 \end{pmatrix}\) = \(\begin{pmatrix} 2 \\ 5 \end{pmatrix}\)
Now, we need to calculate the magnitude or length of the vector (2, 5).
|q - 1/2p| = \(\sqrt{(2)^2 + (5)^2}\) = \(\sqrt{4 + 25}\) = \(\sqrt{29}\)
Therefore, the answer is option D: \(\sqrt{29}\).
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