(a) Make up any point
P(a,b,c)
in
R^(3)
where
a,b
, and
c
are any integers.
(b) Make up scalar equations for any three non-coincident planes
\pi _(1),\pi _(2)
, and
\pi
3, which point P satisfies. Ensure that the planes do not imersect on the same line (you have to prove this in the next part).
(c) Show that the three plases intersect at exactly one point in
R
3, and do not posess other points common to all 3 planes.
(c) Show that the three planes intersect at exactly ome
all thres
(d) Show, using simulancoes equations than evactly one wolution exists for your plane sysucm, namely fhat of point P.
(a) Make up any point
P(a,b,c)
in
R^(3)
where
a,b
, and
c
are any integers.
(b) Make up scalar equations for any three non-coincident planes
\pi _(1),\pi _(2)
, and
\pi _(3)
which point P satisfies. Ensure that the planes do not intersect on the same line (you have to prove this in the next part).
(c) Show that the three planes intersect at exactly one point in
R^(3)
, and do not possess other points common to all three planes.
(d) Show, using simultaneous equations that exactly one solution exists for your plane system, namely that of point
P
.
(a) Make up any point
P(a,b,c)
in
R^(3)
where
a,b
, and
c
are any integers.
(b) Make up scalar equations for any three non-coincident planes
\pi _(1),\pi _(2)
, and
\pi _(3)
which point P satisfies. Ensure that the planes do not intersect on the same line (you have to prove this in the next part).
(c) Show that the three planes intersect at exactly one point in
R^(3)
, and do not posses other points common to all three planes.
(d) Show, using simultaneous equations that exactly one solution exists for your plane system, namely that of point
P
.