# Vector - basic operations

There are given points A [-9; -2] B [2; 16] C [16; -2] and D [12; 18]

a. Determine the coordinates of the vectors u=AB v=CD s=DB
b. Calculate the sum of the vectors u + v
c. Calculate difference of vectors u-v
d. Determine the coordinates of the vector w = -7.u

ux =  11
uy =  18
vx =  -4
vy =  20
sx =  10
sy =  2
(u+v)x =  7
(u+v)y =  38
(u-v)x =  15
(u-v)y =  -2
wx =  -77
wy =  -126

### Step-by-step explanation:

$u=\left(2-\left(-9\right);16-\left(-2\right)\right)=\left(11;18\right)$
${u}_{y}=16-\left(-2\right)=18$
$s=\left(12-\left(2\right);18-\left(16\right)\right)=\left(10;2\right)$
${v}_{y}=18-\left(-2\right)=20$
${s}_{x}=12-\left(2\right)=10$
${s}_{y}=18-\left(16\right)=2$
$u+v=\left(11+\left(-4\right);18+\left(20\right)\right)=\left(7;38\right)$
$\left(u+v{\right)}_{y}=18+\left(20\right)=38$
$u-v=\left(11-\left(-4\right);18-\left(20\right)\right)=\left(15;-2\right)$
$\left(u-v{\right)}_{y}=18-\left(20\right)=-2$
$w=-7.u=\left(-7\cdot \left(11\right);-7\cdot \left(18\right)\right)=\left(-77;-126\right)$

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