Calculate the magnitude of the vector.
This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Here are the solutions to your questions:
a) Find the magnitude and bearing of the vector $\vec{OQ} = \begin{pmatrix} 4 \\ -6 \end{pmatrix}$.
Step 1: Calculate the magnitude of the vector.
The magnitude of a vector $\begin{pmatrix} x \\ y \end{pmatrix}$ is given by $\sqrt{x^2 + y^2}$.
$$ |\vec{OQ}| = \sqrt{4^2 + (-6)^2} $$
$$ |\vec{OQ}| = \sqrt{16 + 36} $$
$$ |\vec{OQ}| = \sqrt{52} $$
$$ |\vec{OQ}| \approx 7.211 $$
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