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Chapter 12: Problem 28

Let \(\mathbf{u}=\langle 4,-2\rangle, \mathbf{v}=\langle-4,6\rangle,\) and \(\mathbf{w}=\langle 0,8\rangle .\) Express the following vectors in the form \(\langle a, b\rangle\) $$\mathbf{u}+\mathbf{v}$$

Short Answer

Expert verified
Answer: The sum of the vectors \(\mathbf{u}+\mathbf{v}\) is \(\langle 0, 4 \rangle\).

Step by step solution

01

Identify the components of each vector

The components of the given vectors are: $$\mathbf{u} = \langle 4, -2 \rangle$$ $$\mathbf{v} = \langle -4, 6 \rangle$$
02

Add the corresponding components of the two vectors

To find the sum \(\mathbf{u} + \mathbf{v}\), we add the x-components and y-components of the vectors separately: $$a = 4 + (-4) = 0$$ $$b = -2 + 6 = 4$$
03

Write the sum in the form \(\langle a, b \rangle\)

Now that we have the sum of the x-components and y-components, we can express the sum of the vectors \(\mathbf{u} + \mathbf{v}\) in the form \(\langle a, b \rangle\): $$\mathbf{u}+\mathbf{v} = \langle 0, 4 \rangle$$

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