Question

1. given the following vector: $mathbf{p} = -2mathbf{i} + 4mathbf{j}$ , find $5mathbf{p}$.
2. given the following vectors: $mathbf{r} = < 3, -4 >$ and $mathbf{s} = < -4, -2 >$ , find $2mathbf{r} - 6mathbf{s}$.

Explanation:

Step1: Multiplicar vector p por 5

$5\mathbf{p} = 5(-2\mathbf{i} + 4\mathbf{j})$
$5\mathbf{p} = 5(-2)\mathbf{i} + 5(4)\mathbf{j}$
$5\mathbf{p} = -10\mathbf{i} + 20\mathbf{j}$

Step2: Calcular 2r para el segundo problema

$2\mathbf{r} = 2\langle 3, -4
angle$
$2\mathbf{r} = \langle 2(3), 2(-4)
angle = \langle 6, -8
angle$

Step3: Calcular 6s para el segundo problema

$6\mathbf{s} = 6\langle -4, -2
angle$
$6\mathbf{s} = \langle 6(-4), 6(-2)
angle = \langle -24, -12
angle$

Step4: Restar 6s a 2r

$2\mathbf{r} - 6\mathbf{s} = \langle 6 - (-24), -8 - (-12)
angle$
$2\mathbf{r} - 6\mathbf{s} = \langle 6 + 24, -8 + 12
angle = \langle 30, 4
angle$

Answer:

1. $-10\mathbf{i} + 20\mathbf{j}$
2. $\langle 30, 4

angle$