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Chapter 12: Problem 11

How do you compute the magnitude of \(\mathbf{v}=\left\langle v_{1}, v_{2}\right\rangle ?\)

Short Answer

Expert verified
Question: Calculate the magnitude of a two-dimensional vector with components \(v_1\) and \(v_2\). Answer: The magnitude of the vector \(\mathbf{v}\) can be computed using the formula \(\| \mathbf{v} \| = \sqrt{(v_1)^2 + (v_2)^2}\).

Step by step solution

01

Identify the vector components

In this exercise, the two components of the vector \(\mathbf{v}\) are \(v_1\) and \(v_2\).
02

Square the components

Calculate the square of each component: \((v_1)^2\) and \((v_2)^2\).
03

Sum the squares

Add the squared components together: \((v_1)^2 + (v_2)^2\).
04

Calculate the square root

To find the magnitude of the vector, compute the square root of the sum of the squares: \(\sqrt{(v_1)^2 + (v_2)^2}\).
05

Write the final answer

Now, we can express the magnitude of the vector \(\mathbf{v}\) as: $$\| \mathbf{v} \| = \sqrt{(v_1)^2 + (v_2)^2}$$.

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