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 answer:

u_x =  11
u_y =  18
v_x =  -4
v_y =  20
s_x =  10
s_y =  2
(u+v)_x =  7
(u+v)_y =  38
(u-v)_x =  15
(u-v)_y =  -2
w_x =  -77
w_y =  -126

Step-by-step explanation:

$u=(2-(-9);16-(-2))=(11;18)$

$u_y=16-(-2)=18$

$s=(12-(2);18-(16))=(10;2)$

$v_y=18-(-2)=20$

$s_x=12-(2)=10$

$s_y=18-(16)=2$

$u+v=(11+(-4);18+(20))=(7;38)$

$(u+v{)}_y=18+(20)=38$

$u-v=(11-(-4);18-(20))=(15;-2)$

$(u-v{)}_y=18-(20)=-2$

$w=-7.u=(-7\cdot (11);-7\cdot (18))=(-77;-126)$

$w_y=-7\cdot (18)=-126$

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