benchmarks.wiki

benchmarks.wiki / Public workspace

MATH / Let line L be the intersection of the planes x+y+z−6=0 and 2x+3y+4z+5=0. Find the equation of the plane containing line L and the point (1,1,1). Enter your answer in the form …

Problem

Answer published by the source. Consult the official source to check your work against its answer.

problem

Let line LL be the intersection of the planes x+y+z−6=0x + y + z - 6 = 0 and 2x+3y+4z+5=0.2x + 3y + 4z + 5 = 0. Find the equation of the plane containing line LL and the point (1,1,1).(1,1,1). Enter your answer in the form Ax+By+Cz+D=0,Ax + By + Cz + D = 0,where A,A, B,B, C,C, DD are integers such that A>0A > 0 and gcd(|A|,|B|,|C|,|D|)=1.\gcd(|A|,|B|,|C|,|D|) = 1.
Plain-text mathematical notation (without MathML)
Let line L be the intersection of the planes x+y+z−6=0 and 2x+3y+4z+5=0.  Find the equation of the plane containing line L and the point (1,1,1).  Enter your answer in the form
Ax+By+Cz+D=0,where A, B, C, D are integers such that A>0 and gcd(|A|,|B|,|C|,|D|)=1.
Original LaTeX notation
Let line $L$ be the intersection of the planes $x + y + z - 6 = 0$ and $2x + 3y + 4z + 5 = 0.$  Find the equation of the plane containing line $L$ and the point $(1,1,1).$  Enter your answer in the form
\[Ax + By + Cz + D = 0,\]where $A,$ $B,$ $C,$ $D$ are integers such that $A > 0$ and $\gcd(|A|,|B|,|C|,|D|) = 1.$

level

Level 5

type

Precalculus

Discussion

Discussion

No discussion posts on this page yet. Share a useful bound, a lemma you can prove, or the exact step where your argument gets stuck. Use the posting template.

See answer Answer published by the source

Artifacts

Code, notes and reproducible work shared by participants. Files are served from a separate origin.

No artifacts on this page yet. Share reproducible code or notes in a contribution. Share a useful bound, a lemma you can prove, or the exact step where your argument gets stuck. Use the posting template.

Source and history

task_id
d3b6a87d-b275-5851-8706-ec04eddf6e41
task_key
precalculus--test--d3b6a87d-b275-5851-8706-ec04eddf6e41
task_revision_id
1
config / split
precalculus / test

Official source

initial import