Answer
$-2$
Work Step by Step
Recall the dot product property for n-dimensional vectors, which states that if $\vec{u}=(u_1,u_2.....u_n)$ and $\vec{v}=(v_1,v_2.....v_n)$, then their dot product is:
$\vec{u}\cdot \vec{v}=u_1v_1+u_2v_2+........u_nv_n$
We are given that $\vec{a}=2j+k;\vec{a}=4i-7j;\vec{c}=i+6j$
Our aim is to find the dot product $\vec{a} \cdot(\vec{c}+\vec{y})$.
Therefore, we have:
$\vec{a} \cdot (\vec{c}+\vec{y})=\lt 0,2,1 \gt \cdot ( \lt1,6,0\gt +\lt 4,-7,0 \gt ) \\= \lt 0,2,1 \gt \cdot \lt5,-1,0\gt \\=(0)(5)+(2)(-1)+(1)(0) \\=-2$
