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A comprehensive guide to understanding and deriving equations of lines and planes in three-dimensional space. It covers the fundamental concepts of direction vectors, normal vectors, parametric equations, and the relationship between points, lines, and planes. Illustrative examples and exercises to solidify understanding.
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WEEK 3 LECTURE I
the (^) equationof a^ line
a givenpoint
yo
of a^ given
b (^) e L I (^2) a
itI
SEE
0Q
2b 2e
x PG
tothe^
equation
feline
Remart (^) If we^ solve^ for above
sgmffia.EE
Write the (^) parametric equation^ of
passing through the^ points^
2 y EE^ 1
yz.pe ziE7FaHeliue too first.ie 2 poit PCI zi if I direction^ vector 7 to^
QQ Cfo 2 i 6 2 57 a b^ C Equation of
frm ez f z E
2 t (^) parameter solution (^) point Q^ 5, 2
to Zo
us L^ 6,2 57 a b^ c
line
f (^) palamete E 2
y z is^ in^ the^ plane naffest
to top
Tofte (^) zo n La^ b^ c TIP x^ X^
Z Zo POTI (^) acx xoi (^) bcy foi CCZ ZT.iq n
the plane Hot b^ yo azo ax^ by t CZ
Given a plane with (^) equation Extle (^) y Ez^ D ex zx yi
s (^) 7IE.gs E what is^ the^ relevance^ of
b (^) c ex 2 I (^37) Answer (^) the vector^ v^ La^
vector to^ the plane with (^) equation ax by
Find the^ equation^ of
plane containing the (^) points PG^ 2,^
2
R (^) C 3
quoth
Q lo^ 2, I
to (^) fo Zo normal vector^ to
n (^) FR x^ poi PR L 3 l o^ C^2 I^47 4 2 3 PQ o 1 Z^ C 27 2 43 L^ l^ O^2
5 g z I ti Ij t2 k n L^4 5 qe Ez (^) of (^) plane I Cx^ Ie
Ef E
1 If
