We have the following vectors
[tex]\begin{gathered} u=5i-j \\ v=2i+j \\ w=i+7j \end{gathered}[/tex]
and we want to find the following
[tex]u\cdot v+u\cdot w[/tex]
1st, we need to find u*v
[tex]\begin{gathered} u\cdot v=u_i\cdot v_i+u_j\cdot v_j=(5\cdot2)+(-1\cdot1) \\ =10+(-1) \\ =9 \end{gathered}[/tex]
2nd, we must calculate u*w
[tex]\begin{gathered} u\cdot w=u_i\cdot w_i+u_j\cdot w_j \\ =(5\cdot1)+(-1\cdot7) \\ =5+(-7) \\ =-2 \end{gathered}[/tex]
Finally, let's find u*v + u*w
[tex]\begin{gathered} u\cdot v+u\cdot w=9+(-2) \\ =9-2 \\ =7 \end{gathered}[/tex]
Thus, the scalar value is 7
