Find the intersection of the line and plane: x+2y+2z=3, r(t)=<2,-3,3>+t<1,3,-3>

Modelfino0g 2022-09-16 Answered
Find the intersection of the line and plane:
x + 2 y + 2 z = 3 r ( t ) =< 2 , 3 , 3 > + t < 1 , 3 , 3 >
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Answers (1)

Raina Russo
Answered 2022-09-17 Author has 20 answers
Equation of plane is:
x + 2 y + 2 z = 3
and Equation of Straight line is:
r ( t ) =< 2 , 3 , 3 > + t < 1 , 3 , 3 >
The cantesian equation of straight line
x 2 1 = y + 3 3 = 7 3 3 = t x = 2 + t   y = 3 t 3   z = 3 3 t
Let the point of intersection be
P ( 2 + t , 3 t 3 , 3 3 t )
So:
P ( 2 + t , 3 t 3 , 3 3 t )
Since the point P lies on the plane
From x + 2 y + 27 = 3 ( 2 + t ) + 2 ( 3 t 3 ) + 2 ( 3 3 t ) = 3 2 + t + 6 t 6 + 6 6 t = 3 t = 3 2 t = 1
put t = 1 x = 2 + 1 = 3
The point of intersection
P = ( 3 , 0 , 0 )

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