Question

What is the component form of the vector represented by 2a when a⃗ =〈−2,3〉?

2a = <__,___>

Answer 1

`\vec v = 2\cdot \vec a = \langle -4,6 \rangle`

Explanation:

Let
`\vec a = \langle -2, 3 \rangle`, we need to determine
`\vec v = 2\cdot \vec a`, which can be found by applying the following property:

`\alpha \cdot \langle x,y \rangle = \langle \alpha \cdot x, \alpha \cdot y\rangle`,
`\forall \,\alpha,x,y\in \mathbb{R}` (1)

Then,

`\vec v = 2\cdot \langle -2,3 \rangle`

`\vec v = \langle -4,6 \rangle`