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

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