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

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.

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

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

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

Final Answer