# 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

Correct result:

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

#### Solution:

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

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Tips to related online calculators
For Basic calculations in analytic geometry is helpful line slope calculator. From coordinates of two points in the plane it calculate slope, normal and parametric line equation(s), slope, directional angle, direction vector, the length of segment, intersections the coordinate axes etc.
Two vectors given by its magnitudes and by included angle can be added by our vector sum calculator.

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