determine whether the lines intersect and if so find the point of intersection,and the cosine of the angle of intersection.
x=4t+2, y=3, z=-t+1
x=2s+2, y=2s+3, z=s+1
all i really need help with is isolating/solving for t and s, it's been a while since solving systems of equations and im not exactly sure what to do here. do I eliminate the parameter first? then how do i find x and z? and what does y=3 mean? some help would be great :)
x=4t+2, y=3, z=-t+1
x=2s+2, y=2s+3, z=s+1
all i really need help with is isolating/solving for t and s, it's been a while since solving systems of equations and im not exactly sure what to do here. do I eliminate the parameter first? then how do i find x and z? and what does y=3 mean? some help would be great :)
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line l : (2,3,1)+t(4,0,-1)
line ll :(2,3,1)+s(2,2,1)
4t+2=2s+2
2t+1=s+1
s=2t
--------------
2s+3=3
s=0
------------
-t+1=s+1
-t=s
-t=0 =>t=0
s=2t =>s=2(0)=0 OK
they intersect at (2,3,1)
-----------------
cosα=|(4,0,-1)*(2,2,1)|/√(4)²+(0)²+(-1)…
cosα = |8+0-1|/√17√9
cosα =7/3√17
α =55.53°
-------------
Note:At the written that it is in ...
is √(4)²+(0)²+(-1)²√(2)²+(2)²+(1)²
line ll :(2,3,1)+s(2,2,1)
4t+2=2s+2
2t+1=s+1
s=2t
--------------
2s+3=3
s=0
------------
-t+1=s+1
-t=s
-t=0 =>t=0
s=2t =>s=2(0)=0 OK
they intersect at (2,3,1)
-----------------
cosα=|(4,0,-1)*(2,2,1)|/√(4)²+(0)²+(-1)…
cosα = |8+0-1|/√17√9
cosα =7/3√17
α =55.53°
-------------
Note:At the written that it is in ...
is √(4)²+(0)²+(-1)²√(2)²+(2)²+(1)²