Question

what is the magnitude of \\(\vec{w}\\)? \\(\vec{w}\\) has terminal point (12,2). \\(\vert \vec{w}\vert = ?\\) round your answer to the nearest hundredth.

Explanation:

Step1: Recall the formula for the magnitude of a vector

The magnitude of a vector \(\vec{w} = (x, y)\) is given by \(|\vec{w}|=\sqrt{x^{2}+y^{2}}\).

Step2: Identify the components of the vector

From the given point \((12, 2)\), we have \(x = 12\) and \(y=2\).

Step3: Substitute the values into the formula

Substitute \(x = 12\) and \(y = 2\) into the formula:

$$ |\vec{w}|=\sqrt{12^{2}+2^{2}}=\sqrt{144 + 4}=\sqrt{148} $$

Step4: Calculate the numerical value

\(\sqrt{148}\approx12.1655\), and rounding to the nearest hundredth gives \(12.17\).

Answer:

\(12.17\)