How do I use the methods in the example to solve question 10? 10. Suppose that II1 and II2 are parallel planes in R³, given by:II1 : ajx + b¡y+cjz = d1, and II2 : ajx + b¡y+cjz = d2,where di + d2. Now, suppose that II3 is another plane given by:d3,II3 : a3x + b3y + C3z||which is not parallel to II1 or II2. Show that the line of intersection between II, and II3is parallel to the line of intersection of II2 and II3. Consult Section 1.2 for the definitionof parallel lines in R³. 1.6 " 10 3 TT, n panlel to lla, x+ b,yt s: ,7o Gind the interseckim f TT, ad TT,sodvee Ao bi where A =6。ュTo find the hatersectim f ?12 w TTg->selve Ax= b,ahere A 'n as abony andSuce wtgiven that T, is not parallel to TT, theSystem [A;b, ] is eonsistent, ad hasaninfinteSodutions.Since the itersection 'n nNine, A hayfree variable Assume that it is z.exactly oueThen the RREFf [A:]leaks 1ke1pか Pand the RREFloons lke Lonow, salve these aad show the lines(* WLOG means.KwithoutmeAAsare parallel.loss of genunality"--the argument is dontisalwh ether it is Ry y a z,

If ∏1: a1x+b1y+c1z=d1 and ∏2: a2x+b2y+c2z=d2 are parallel planes, then, the cross product ∏1×∏2=0.…

Suppose that II1 and II2 are parallel planes in R³, given by: II : ajx + biy +cjz = d1, and II2 : ajx + b1y + c1z = d2, %3D where di + d2. Now, suppose that II3 is another plane given by: II3 : azx + b3y + c3z = d3, which is not parallel to II1 or II2. Show that the line of intersection between II and II3 is parallel to the line of intersection of II2 and II3. Consult Section 1.2 for the definition of parallel lines in R³.

Suppose that II1 and II2 are parallel planes in R³, given by: II : ajx + biy +cjz = d1, and II2 : ajx + b1y + c1z = d2, %3D where di + d2. Now, suppose that II3 is another plane given by: II3 : azx + b3y + c3z = d3, which is not parallel to II1 or II2. Show that the line of intersection between II and II3 is parallel to the line of intersection of II2 and II3. Consult Section 1.2 for the definition of parallel lines in R³.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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How do I use the methods in the example to solve question 10?

10. Suppose that II1 and II2 are parallel planes in R³, given by:
II1 : ajx + b¡y+cjz = d1, and II2 : ajx + b¡y+cjz = d2,
where di + d2. Now, suppose that II3 is another plane given by:
d3,
II3 : a3x + b3y + C3z
||
which is not parallel to II1 or II2. Show that the line of intersection between II, and II3
is parallel to the line of intersection of II2 and II3. Consult Section 1.2 for the definition
of parallel lines in R³.

1.6 " 10 3 TT, n panlel to ll
a, x+ b,yt s: ,
7o Gind the interseckim f TT, ad TT,
sodve
e Ao bi where A =
6。ュ
To find the hatersectim f ?12 w TTg
->
selve Ax= b,
ahere A 'n as abony and
Suce wt
given that T, is not parallel to TT, the
System [A;b, ] is eonsistent, ad has
aninfinte
Sodutions.
Since the itersection 'n n
Nine, A hay
free variable Assume that it is z.
exactly oue
Then the RREFf [A:]
leaks 1ke
1pか P
and the RREF
loons lke Lo
now, salve these aad show the lines
(* WLOG means.
Kwithout
meAAs
are parallel.
loss of genunality"
--
the argument is dontisal
wh ether it is Ry y a z,

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