## burhan101 2 years ago Which line is the same as [x, y]=[1, -8] + t[ 4,-3]? A [x, y] =[2, 4] +t[-4, 3] B [x, y] =[13, 17]+t[8, -6]

1. burhan101

And how do you figure it out?

2. completeidiot

you could just determine the line equation y(x), through substitution

3. burhan101

@completeidiot how ?

4. completeidiot

[x, y]=[1, -8] + t[ 4,-3] x=1+4t y=-8-3t solve for t for one of the equations, then substitute

5. burhan101

by elimination ? @completeidiot

6. sami-21

look for the coefficients of parallel vector. if they are same means either same line or parallel

7. burhan101

@sami-21 what do you mean ?

8. sami-21

look the coefficients of parameter t . each line in space has parallel vector to describe it . so if the vectors are same then lts same .

9. sami-21

in other words i am saying compare following x=1+4t y=-8-3t with A x=2-4t y=4+3t and B x=13+8t y=17-6t

10. sami-21

did you get it ?

11. burhan101

im trying to understand it :S

12. sami-21

well, let me show you how B is same as the given line. each line in the space requires one point and vector to completely define it the coefficients of the t represents that vector so if the coefficients of the t are same or scalar multiple of some number then lines are definitely same . so the vector parallel to given line is (coefficients of t ) v1=<4,-3> vector paralel to line A (coefficients of t ) vA=<-4,3> vector parallel to line B (coefficients of t ) vB=<8,-6> you can see that the vetor Vb parallel to line B is 2 times the vector parallel to given line vB=2v1 it means given line and line |B are identical. Hope its clear now .

13. burhan101

Like how do i compare the parametric equations of A and B. Is there something i sub in ?

14. completeidiot

no i meant solve for t... x=1+4t x-1=4t t=(x-1)/4 y=-8-3t y=-8-3((x-1)/4)