Question #211904

Let L be the line given by <3,-1,2>+t<1,1,-1>,for tER.

1.show that the above line L lies on the plane -2x+3y-4z+1=0.

2.find an equation for the plane through the point p=(3,-2,4) that is perpendicular to the line <-8,2,0>+t<-3,2,-7>.


1
Expert's answer
2021-06-30T08:47:50-0400

1.


x=3+t,y=1+t,z=2tx=3+t, y=-1+t, z=2-t

2x+3y4z+1-2x+3y-4z+1

=2(3+t)+3(1+t)4(2t)+1=-2(3+t)+3(-1+t)-4(2-t)+1

=2(3+t)+3(1+t)4(2t)+1=-2(3+t)+3(-1+t)-4(2-t)+1

=5t16=5t-16

Consider t=0t=0


5t16=5(0)16=1605t-16=5(0)-16=-16\not=0

Therefore the line L does not lie on the plane 2x+3y4z+1=0.-2x+3y-4z+1=0.


2.


n=3,2,7\vec n=\langle-3, 2, -7\rangle

Point P=(3,2,4).P=(3,-2,4).

The equation for the plane through the point P=(3,2,4)P=(3,-2,4) that is perpendicular to the line 8,2,0+t3,2,7\langle-8, 2, 0\rangle+t\langle-3, 2, 7\rangle is


3(x3)+2(y(2))7(z4)=0-3(x-3)+2(y-(-2))-7(z-4)=0

or


3x2y+7z41=03x-2y+7z-41=0




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Comments

Assignment Expert
16.07.21, 00:09

Dear Nhlanhla Muthwam the direction vector of the straight line <-8,2,0>+t<-3,2,-7> is <-3,2,-7>, the straight line is perpendicular to the plane, that is why n=<-3,2,-7>.


Nhlanhla Muthwa
06.07.21, 14:53

How to did you get n=⟨−3,2,−7⟩?

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