# 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

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:

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

Leave us a comment of this math problem and its solution (i.e. if it is still somewhat unclear...):