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Chapter 6: Problem 10

Suppose \(\mathbf{u}=(-4,5)\) and \(\mathbf{v}=(2,-6) .\) Compute \(\mathbf{u} \cdot \mathbf{v}\).

Short Answer

Expert verified
The dot product of the vectors \(\mathbf{u}=(-4,5)\) and \(\mathbf{v}=(2,-6)\) is \(\mathbf{u} \cdot \mathbf{v} = -38\).

Step by step solution

01

Write down the given vectors

We are given two vectors: \[\mathbf{u} = (-4, 5)\] \[\mathbf{v} = (2, -6)\]
02

Compute the dot product

Apply the formula to calculate the dot product of \(\mathbf{u}\) and \(\mathbf{v}\): \[\mathbf{u} \cdot \mathbf{v} = (-4) \cdot (2) + (5) \cdot (-6) = -8 - 30\]
03

Calculate the final result

From the calculation above, we get: \[\mathbf{u}\cdot \mathbf{v} = -8 - 30 = -38\] Thus, the dot product of the given vectors \(\mathbf{u}\) and \(\mathbf{v}\) is \(-38\).

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