system and point of intersection?

[real_name_x]

when you have 3 systems.. for ex
x + 2y +3z =5
2x - y + 2z = 7
3x - 3y + 2z = 10

ok and they say "find the coordinates of the point of intersection of the planes"

that just means you have to solve for x y z right ? and each value is a coordinate of intersection ? right? im not sure.

so if im right. and lets say X was = to 2, then one coordinate would be {2, 0, 0} right?

thanks

 

[tkhunny]

You must solve it to see the answers to your questions. You can get a single point, a line, a whole plane, or nothing at all. It depends on the system of equations. Let's see how you attack it.

 

[Denis]

when you have 3 systems.. for ex
x + 2y +3z =5
2x - y + 2z = 7
3x - 3y + 2z = 10
ok and they say "find the coordinates of the point of intersection of the planes"
that just means you have to solve for x y z right ? and each value is a coordinate of intersection ? right? im not sure.
so if im right. and lets say X was = to 2, then one coordinate would be {2, 0, 0} right?

Quit beating around the bush, and solve this system for x, y and z:
x + 2y +3z =5
2x - y + 2z = 7
3x - 3y + 2z = 10
That means find a value for x, and y, and z, that "fits" all 3 equations.

If you have no idea how to start, then you need classroom help.

 

[pka]

\(\displaystyle \left( {\begin{array}{rrr}
1 & 2 & 3 \\
2 & { - 1} & 2 \\
3 & { - 3} & 2 \\
\end{array}} \right)^{ - 1} = \left( {\begin{array}{rrr}
{ - 4} & {13} & { - 7} \\
{ - 2} & 7 & { - 4} \\
3 & { - 9} & 5 \\
\end{array}} \right)\)

\(\displaystyle \left( {\begin{array}{rrr}
{ - 4} & {13} & { - 7} \\
{ - 2} & 7 & { - 4} \\
3 & { - 9} & 5 \\
\end{array}} \right)*\left( {\begin{array}{c}
5 \\
7 \\
{10} \\
\end{array}} \right) = \left( {\begin{array}{c}
1 \\
{ - 1} \\
2 \\
\end{array}} \right)\)

Therefore,, \(\displaystyle x=1,\: y=-1,\;z=2\).