# Question #4bd8a

Oct 4, 2016

$2 \vec{U} - 3 \vec{V} = \left(7 , - 21\right) .$

#### Explanation:

We have to use the following Defn. of Multiplication of a Vector by

a Scalar :

$\text{Defn. : Let vector "vecu=(u_1,u_2)" and let } k \in \mathbb{R} .$ Then,

Multiplication of $\vec{u}$ by (scalar) $k ,$ denoted by, $k \vec{u} ,$ is,

defined as, $k \vec{u} = k \left({u}_{1} , {u}_{2}\right) = \left(k {u}_{1} , k {u}_{2}\right) .$

I hope that Vector Addition / Subtraction is known.

So, with vectors $\vec{U} = \left(2 , - 3\right) \mathmr{and} \vec{V} = \left(- 1 , 5\right) ,$ we have,

$2 \vec{U} - 3 \vec{V} = 2 \left(2 , - 3\right) - 3 \left(- 1 , 5\right) = \left(4 , - 6\right) - \left(- 3 , 15\right)$

$= \left(4 + 3 , - 6 - 15\right)$

$\therefore 2 \vec{U} - 3 \vec{V} = \left(7 , - 21\right) .$