Questions: Find the sum of the given vectors. a = ⟨-5, 5⟩, b = ⟨7, -2⟩ Illustrate geometrically.

Find the sum of the given vectors. a = ⟨-5, 5⟩, b = ⟨7, -2⟩ Illustrate geometrically.
Transcript text: Find the sum of the given vectors. \[ \mathbf{a}=\langle-5,5\rangle, \quad \mathbf{b}=\langle 7,-2\rangle \] Illustrate geometrically.
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Solution

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Solution Steps

To find the sum of the given vectors \(\mathbf{a}\) and \(\mathbf{b}\), we need to add their corresponding components. Specifically, we add the x-components together and the y-components together.

Step 1: Define the Vectors

We are given two vectors: \[ \mathbf{a} = \langle -5, 5 \rangle \] \[ \mathbf{b} = \langle 7, -2 \rangle \]

Step 2: Add the Vectors

To find the sum of the vectors \(\mathbf{a}\) and \(\mathbf{b}\), we add their corresponding components: \[ \mathbf{a} + \mathbf{b} = \langle -5 + 7, 5 + (-2) \rangle \]

Calculating the components: \[ \mathbf{a} + \mathbf{b} = \langle 2, 3 \rangle \]

Step 3: Present the Result

The sum of the vectors is: \[ \mathbf{a} + \mathbf{b} = \langle 2, 3 \rangle \]

Final Answer

\(\boxed{\langle 2, 3 \rangle}\)

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