Every vector has a magnitude, also called modulus. In this section we learn how to calculate the magnitude of a vector.
Given a vector \(\vec{v} = \begin{pmatrix}x \\ y \end{pmatrix}\), its magnitude, also called modulus can be calculated with the formula: \[\begin{vmatrix}\vec{v} \end{vmatrix} = \sqrt{x^2 + y^2}\]
In this tutorial we learn how to calculate the magnitude of a vector.
Given the two vector \(\vec{a} = \begin{pmatrix}1 \\ 3 \end{pmatrix}\) we can calculate its magnitude as follows: \[\begin{aligned} \begin{vmatrix} \vec{a} \end{vmatrix} & = \sqrt{1^2 + 3^2} \\ & = \sqrt{1 + 9} \\ \begin{vmatrix} \vec{a} \end{vmatrix} & = \sqrt{10} \quad \begin{pmatrix} \approx 3.16 \end{pmatrix} \end{aligned}\]
Find and write the exact value of the magnitude for each of the vectors, shown below. When applicable: also use your calculator to round your answers to two decimal places (2 d.p).
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