Direction vector

The line p is given by the point P [- 0,5; 1] and the direction vector s = (1,5; - 3) determines:
A) value of parameter t for points X [- 1,5; 3], Y [1; - 2] lines p
B) whether the points R [0,5; - 1], S [1,5; 3] lies on the line p
C) parametric equations of the line m || p if the line m passes through the origin of the coordinate system
D) parametric equations of the line n _ | _ p, if the line n passes through the point N [- 2; 4]

Result

t1 =  -0.6667
t2 =  1
R=



t2 =S=



t2 =mx = 1.5t
my = -3t
nx = -2+3t
ny = 4-1.5t

Step-by-step explanation:

Px=0.5;Py=1 sx=1.5;sy=3  X[1,5;3] 1.5=Px+t1 sx  t1=(1.5Px)/sx=(1.5(0.5))/1.5=0.6667
Y[1;2] 1=Px+t1 sx  t2=(1Px)/sx=(1(0.5))/1.5=1
R[0,5;1] p1=(0.5Px)/sx=(0.5(0.5))/1.5=320.6667 p2=(1Py)/sy=(11)/(3)=320.6667 p1=p2 R=1
S[1,5;3] p3=(1.5Px)/sx=(1.5(0.5))/1.5=34=1311.3333 p4=(3Py)/sy=(31)/(3)=320.6667 p3=p4 S=0
mx=mx=1.5t
my=my=3t
(1.5;3)(3;1.5) nx=nx=2+3t
ny=ny=41.5t



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