assigned work: pg. 449 #1abc, 2abc, 5, 7-9,12,15 write out what “you think” the vector,...
TRANSCRIPT
Assigned work: pg. 449 #1abc, 2abc, 5, 7-9,12,15
Write out what “you think” the vector, parametric a symmetric equations of a line in R3 would be.
8.3 Vector, Parametric & Symmetric Equations of a Line in R3
In R3:
0
0 0 0
:
( , , ) ( , , ) ( , , )
Vector Equation
r r dt
x y z x y z a b c t
8.3 Vector, Parametric & Symmetric Equations of a Line in R3
In R3:
0
0
0
Parametric Equation
x x at
y y bt t R
z z ct
8.3 Vector, Parametric & Symmetric Equations of a Line in R3
In R3:
0 0 0 , , 0x x y y z z
a b ca b c
Symmetric Equation
8.3 Vector, Parametric & Symmetric Equations of a Line in R3
Ex 1: Find a direction vector for:
a)The line that passes through P(6,-4,1) & Q(2,-8,-5)
b)A line perpendicular to the xz plane.
a)
b)
( 4, 4, 6)
(2,2,3)
PQ OQ OP
reduce direction vector
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(0,1,0) (sin
)
ce perpendicular to xz
planeis parallel to y axis
8.3 Vector, Parametric & Symmetric Equations of a Line in R3
Ex 2: Find vector, parametric & symmetric equations of the line which passes through A(2,-2,-8) and B(5,-2,-14).
2 82
1 2
(3,0, 6) (1,0, 2)
(2, 2, 8) (1,0, 2)
2
2
8 2
( )x z
y
AB therefore d
r t Vector
x t
y Parametric
z t
Symmetric Equation solve for t
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