For $\mathbf{u}=\langle 3,-1\rangle, \mathbf{v}=\langle 2,1\rangle$, and $\mathbf{w}=\langle 1,4\rangle$, evaluate the expression.
\[
u \cdot v-u \cdot w
\]
\[
u \cdot v-u \cdot w=
\]
(Simplify your answer.)

Step 1 ：Given vectors are: \(\mathbf{u} = \langle 3,-1 \rangle\), \(\mathbf{v} = \langle 2,1 \rangle\), and \(\mathbf{w} = \langle 1,4 \rangle\)

Step 2 ：We need to evaluate the expression \(u \cdot v - u \cdot w\)

Step 3 ：The dot product of two vectors is calculated by multiplying the corresponding entries of the two vectors and then adding those products

Step 4 ：Calculate the dot product of vectors u and v: \(u \cdot v = 3*2 + (-1)*1 = 5\)

Step 5 ：Calculate the dot product of vectors u and w: \(u \cdot w = 3*1 + (-1)*4 = -1\)

Step 6 ：Subtract the dot product of vectors u and w from the dot product of vectors u and v: \(u \cdot v - u \cdot w = 5 - (-1) = 6\)

Step 7 ：Final Answer: \(\boxed{6}\)