In Exercises 21–38, let u = 2i - 5j, v = -3i + 7j, and w = -i - 6j. Find each specified vector or scalar.
u - v

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Identify the given vectors: \( \mathbf{u} = 2\mathbf{i} - 5\mathbf{j} \) and \( \mathbf{v} = -3\mathbf{i} + 7\mathbf{j} \).

Recall that vector subtraction \( \mathbf{u} - \mathbf{v} \) is performed by subtracting the corresponding components of \( \mathbf{v} \) from \( \mathbf{u} \).

Subtract the \( \mathbf{i} \)-components: \( 2 - (-3) = 2 + 3 \).

Subtract the \( \mathbf{j} \)-components: \( -5 - 7 = -5 - 7 \).

Write the resulting vector as \( (2 + 3)\mathbf{i} + (-5 - 7)\mathbf{j} \), which is the vector \( \mathbf{u} - \mathbf{v} \).

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