Answer
$\lt 0,28,14 \gt$
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 $\vec{a}=2j+k = \lt0,2,1\gt$ and $\vec{b}=-3i+5j+4k =\lt-3,5,4\gt$
Our aim is to find the dot product $(\vec{a} \cdot \vec{b}) \vec{a}$.
Therefore, we have:
$(\vec{a} \cdot \vec{b}) \vec{a}= (\lt 0,2,1 \gt \cdot \lt -3,5,40\gt) \lt 0,2,1 \gt \\= [(0)(-3)+(2)(5)+(1)(4)) \lt 0,2,1 \gt \\=(14) \lt 0,2,1 \gt\\=\lt 0,28,14 \gt$