Answer:
[tex]\vec v = 2\cdot \vec a = \langle -4,6 \rangle[/tex]
Step-by-step explanation:
Let [tex]\vec a = \langle -2, 3 \rangle[/tex], we need to determine [tex]\vec v = 2\cdot \vec a[/tex], which can be found by applying the following property:
[tex]\alpha \cdot \langle x,y \rangle = \langle \alpha \cdot x, \alpha \cdot y\rangle[/tex], [tex]\forall \,\alpha,x,y\in \mathbb{R}[/tex] (1)
Then,
[tex]\vec v = 2\cdot \langle -2,3 \rangle[/tex]
[tex]\vec v = \langle -4,6 \rangle[/tex]
