Question

what is the magnitude of \\( \vec { v } \\)?
round your answer to the nearest hundredth.

Explanation:

Step1: Recall the formula for the magnitude of a vector

The magnitude of a vector \(\vec{v} = (x, y)\) is given by \(|\vec{v}|=\sqrt{x^{2}+y^{2}}\). Here, \(x = 10\) and \(y=17\).

Step2: Substitute the values into the formula

Substitute \(x = 10\) and \(y = 17\) into the formula: \(|\vec{v}|=\sqrt{10^{2}+17^{2}}\).
First, calculate \(10^{2}=100\) and \(17^{2} = 289\). Then, \(10^{2}+17^{2}=100 + 289=389\).
So, \(|\vec{v}|=\sqrt{389}\).

Step3: Calculate the square root and round

Calculate \(\sqrt{389}\approx19.72\) (rounded to the nearest hundredth).

Answer:

\(19.72\)