Find an equation for the plane that (a) is perpendicular

Joseph Krupa 2021-12-15 Answered
Find an equation for the plane that
(a) is perpendicular to f{v} = (1, 1, 1f{v}=(1,1,1) and passes through (1,0,0).
(b) is perpendicular to f{v} = (1, 2, 3f{v}=(1,2,3) and passes through (1,1,1).
(c) is perpendicular to the line f{l}(t) = (5, 0, 2)t + (3, −1, 1f{l}(t)=(5,0,2)t+(3,1,1) and passes through (5, −1, 0)(5,−1,0).
(d) is perpendicular to the line f{l}(t) = (−1, −2, 3)t + (0, 7, 1f{l}(t)=(1,2,3)t+(0,7,1) and passes through (2, 4, −1)(2,4,−1).
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Expert Answer

sonorous9n
Answered 2021-12-16 Author has 34 answers
a) n=(1,1,1) where n is the normal to the plane that passes through (1,0,0)
Using the equation of the plane we get:
1(x1)+1(y0)+1(z0)=0
x+y+z1=0
b) n=(1,2,3) where n is the normal to the plane that passes through (1,1,1)
Using the equation of the plane we get
1(x1)+2(y1)+3(z1)=0
x+2y+3z6=0

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Raymond Foley
Answered 2021-12-17 Author has 39 answers
c) n= direction of line =(5,0,2) where n is the normal to the plane that passes through (5,1,0)
Using the equation of the plane we get:
5(x5)+0(y+1)+2(z0)=0
5x+2z25=0
d) n= direction of line =(1,2,3) where n is the normal to the plane that passes through (2,3,-1)
Using the equation of the plane we get:
1(x2)2(y4)+3(z+1)=0
x2y+3z+13=0

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