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frx
 3 years 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.
frx
 3 years 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.

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amistre64
 3 years ago
Best ResponseYou've already chosen the best response.2it sounds doable, but its hard to make out what its actually asking for

frx
 3 years ago
Best ResponseYou've already chosen the best response.0New 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.

amistre64
 3 years ago
Best ResponseYou've already chosen the best response.2we 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 ??

amistre64
 3 years ago
Best ResponseYou've already chosen the best response.2the line equation parts are x = 4 + 3n y = 1 + an z = 3 +2n

frx
 3 years ago
Best ResponseYou've already chosen the best response.0I 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

amistre64
 3 years ago
Best ResponseYou've already chosen the best response.2hmm, then we might be able to use x and y to solve for n, and use n to solve for a ... is my idea

frx
 3 years ago
Best 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 \[t,s \in \]

amistre64
 3 years ago
Best ResponseYou've already chosen the best response.2x = 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

amistre64
 3 years ago
Best 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

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