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For which value on the real constant a were the line L intersects the point (4,1,3), with the direction vector (3,a,2), the plane \[(x,y,z)=(1+t2s, 2t+s,1+3t+as), t,s \in \mathbb{R}\] in one point.
 one year ago
 one year ago
For which value on the real constant a were the line L intersects the point (4,1,3), with the direction vector (3,a,2), the plane \[(x,y,z)=(1+t2s, 2t+s,1+3t+as), t,s \in \mathbb{R}\] in one point.
 one year ago
 one year ago

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amistre64Best ResponseYou've already chosen the best response.2
it sounds doable, but its hard to make out what its actually asking for
 one year ago

frxBest ResponseYou've already chosen the best response.0
New formulation: For which values of the real constant a does the line L ( L goes trough the point (4,1,3) and has the direction vector (3,a,2)) intersect the plane \[(x,y,z)=(1+t2s, 2t+s,1+3t+as), t,s \in \mathbb{R}\] in one point.
 one year ago

amistre64Best ResponseYou've already chosen the best response.2
we might wanna try to redefine the plane in a format thats easier to parse. (x,y,z)=(1+t−2s,2t+s,1+3t+as),t,s x = (1+t−2s,2t+s,1+3t+as) y = t z = s is there a way to construct that as: a(xxo)+b(yyo)+c(zzo)=0 ??
 one year ago

amistre64Best ResponseYou've already chosen the best response.2
the line equation parts are x = 4 + 3n y = 1 + an z = 3 +2n
 one year ago

frxBest ResponseYou've already chosen the best response.0
I think it's x=1+t2s, y= 2t+s, z=1+3t+as and the t,s is just to say that thet are Real
 one year ago

amistre64Best ResponseYou've already chosen the best response.2
hmm, then we might be able to use x and y to solve for n, and use n to solve for a ... is my idea
 one year ago

frxBest ResponseYou've already chosen the best response.0
\[(x,y,z)=(1+t2s),2t+s, 1+3t+as)\] \[x=1+t2s\] \[y=2t+s\] \[z=1+3t+as\] where \[t,s \in \]
 one year ago

amistre64Best ResponseYou've already chosen the best response.2
x = 4 + 3n y = 1 + an z = 3 +2n and x = 1 + t  2s y = 0 + 2t + s z = 1 + 3t + as (3 + t  2s)/3 = n (1 + 2t + s)/a = n (2 + 3t + as)/2 = n
 one year ago

amistre64Best ResponseYou've already chosen the best response.2
(3 + t  2s)/3 = n (1 + 2t + s)/a = (3 + t  2s)/3 (2 + 3t + as)/2 = (3 + t  2s)/3 a = (3 + 6t + 3s)/(3 + t  2s) 6 + 9t + 3s(3 + 6t + 3s)/(3 + t  2s) = 6 + 2t  4s 7t +4s + 3s(3 + 6t + 3s)/(3 + t  2s) = 0 21t + 7t^2  14ts 12s + 4st  8s^2 + 9s +18st + 9s^2 = 0 21t + 7t^2 21s + s^2 +8st = 0 7t^221t + s^2 21s+8st = 0 needs more shuffling, but i believe thats the right idea to take
 one year ago

frxBest ResponseYou've already chosen the best response.0
I think I get the idea, will have to spend some time on i tough, thank you for your help! :)
 one year ago
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