Find an equation for the plane that (a) is perpendicular to v=(1,1,1) and passes through (1,0,0). (b) is perpendicular to v=(1,2,3) and passes through

Armorikam

Armorikam

Answered question

2021-05-16

Find an equation for the plane that
(a) is perpendicular to v=(1,1,1) and passes through (1,0,0).
(b) is perpendicular to v=(1,2,3) and passes through (1,1,1)
(c) is perpendicular to the line l(t)=(5,0,2)t+(3,1,1) and passes through (5,-1,0)
(d) is perpendicular to the line l(t)=(1,2,3)t+(0,7,1) and passes through (2,4,-1).

Answer & Explanation

tabuordg

tabuordg

Skilled2021-05-17Added 99 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
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 (2,4,-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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