Question

Find an equation of a plane containing the line r=(-1,5,-4) + t(9,6,-3) which is parallel to the plane -3x + 2y - 5y +28 in which the coefficient of x is -3.

Answer 1

if you cross the direction vector of the line with the normal of the plane you will get a new vector that you can anchor to the lines point to define another point in the parallel plane

Answer 2

lol, thats a bad drawing

Answer 3

my idea might have a flaw in it .....

Answer 4

i got the normal vector which is (-3,2,-5)? and then Po=(-1,5,-4)? then used the dot product so that -3(1-x)-2(5-y)-5(-4-z)=o but it keeps saying its wrong? how do i get a new vector from the normal vector?

Answer 5

direction vector of the line is: <9,6,-3>, or reduced to <3,2,-1>

the normal vector is as you stated: <-3,2,-5>

my idea is to cross these 2 vectors to find a new vector but I cant really see it being able to define a parallel plane perse. I can develop a perpendicular place tho

Answer 6

the dot product of the normal and direction vectors is:

3, 2,-1
-3,2,-5
--------
-9+4+5 = 0 so the vetcors themselves are already perped to each other

Answer 7

so basically its asking to use the normal given and the point given to define a parallel plane

Answer 8

ok so how would i get the equation of the plane?

Answer 9

-3(x-px) + 2(y-py) - 5(z-pz) + d = 0

Answer 10

the +d was spurious on my part, im abit sick today :)

given point is: (-1,5,-4)

-3(x+1) + 2(y-5) - 5(z+4) = 0

-3x-3
+2y-10
- 5z-20

-3x + 2y -5z -33 = 0

your setup was fine except it starts with a +3x not a -3x

Answer 11

thank you so much :) it was right