Dawson Downs

Dawson Downs

Answered

2022-07-15

Solve the following linear system in 3-space.
l 1 : ( x , y , z ) = ( 6 , 0 , 5 ) + s ( 1 , 2 , 3 ) l 2 : ( x , y , z ) = ( 1 , 7 , 14 ) + t ( 3 , 1 , 1 )
My attempt:
First, I converted l 1 and l 2 to the parametric form, which is:
l 1 : { x 1 = 6 + s y 2 = 2 s z 1 = 5 + 3 s l 2 : { x 2 = 1 3 t y 2 = 7 + t z 2 = 14 + t
Then I set x 1 = x 2 and got s+3t=−19.
Then did the same for y 1 and y 2 (2s−t=7), and z 1 and z 2 (3s−t=9)
From there I got stuck. Any help?

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Answer & Explanation

coolng90qo

coolng90qo

Expert

2022-07-16Added 14 answers

It is
s+3t=−7
2s−t=7
3s−t=9

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Stephanie Hunter

Stephanie Hunter

Expert

2022-07-17Added 3 answers

Setting components equal,
(1) 6 + s = 1 3 t
(2) 2 s = 7 + t
(3) 5 + 3 s = 14 + t .
Multiply (1) by 2 and subtract (2) to get 12=−9−7t, or t=−3, and then use (2) to find s=2.
Observe that (3) also holds with these s and t values.
You mistakenly said 18 + s = 1 3 t

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