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# Vectors - Planes

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1. The plane P3 contains both the point a = (3, 2, 2) and the line L which is givenby r = (0, 1, 2) + m(3, 1, −1).

I'm trying to work out the direction of the point a and 0,1,2 call this point b

I did -0A + 0B = -3,-1,0

why is this incorrect?
2. (Original post by khanpatel321)
The plane P3 contains both the point a = (3, 2, 2) and the line L which is givenby r = (0, 1, 2) + m(3, 1, −1).

I'm trying to work out the direction of the point a and 0,1,2 call this point b

I did -0A + 0B = -3,-1,0

why is this incorrect?
Did you have consider that r has a direction vector, showed by the parameter m? did you make a sketch to get an overview?
3. (Original post by Kallisto)
Did you have consider that r has a direction vector, showed by the parameter m? did you make a sketch to get an overview?
Yeah I have one direction 3,1,-1

now looking for the second so I can cross product them to get the normal.

The second direction ab that is how I worked it out but it is wrong.
4. Well, if point A (3,2,2)and the point P (0,1,2) <-- taken from the equation of the line L you gave (I could have used any point so long as it lies on L). Then if you work out AP then you also find another line that lies on the plane. You can then do cross product and find Cartesian equation.
5. (Original post by khanpatel321)
Yeah I have one direction 3,1,-1

now looking for the second so I can cross product them to get the normal.

The second direction ab that is how I worked it out but it is wrong.
Hmm... do you know in what a plane (x1x2, x2x3, or x1x3) it is? can you find it out at least? if so, I have an idea.
6. (Original post by khanpatel321)
I did -0A + 0B = -3,-1,0

why is this incorrect?
Why do you think it is incorrect?

You now have two direction vectors that lie in the plane, (3,1,-1) and (-3,-1,0).
7. (Original post by khanpatel321)
x
Erm... just to make it clear for myself: when you wrote about a plane, did you mean a flying means of transport which refers to mathematical aspects, or did you mean an area in a Cartesian coordinate system only? if its the latter one, I misunderstood you, my bad.
8. (Original post by ghostwalker)
Why do you think it is incorrect?

You now have two direction vectors that lie in the plane, (3,1,-1) and (-3,-1,0).
I get an answer of r.(1,-3,-6) = -15

but in the mark scheme it says

(Original post by Kallisto)
Erm... just to make it clear for myself: when you wrote about a plane, did you mean a flying means of transport which refers to mathematical aspects, or did you mean an area in a Cartesian coordinate system only? if its the latter one, I misunderstood you, my bad.

yeah no prob.
9. (Original post by khanpatel321)
I get an answer of r.(1,-3,-6) = -15

but in the mark scheme it says
You've made a slip in your working somewhere.

Using the two direction vectors I previously quoted, I got the normal to be -i+3j (you'll get that or i-3j depending which way round you did the vector product) and the final equaiton x - 3y = -3, as per markscheme.

Post some working if you'd like someone to check it.

Edit: Last post for today.
10. (Original post by ghostwalker)
You've made a slip in your working somewhere.

Using the two direction vectors I previously quoted, I got the normal to be -i+3j (you'll get that or i-3j depending which way round you did the vector product) and the final equaiton x - 3y = -3, as per markscheme.

Post some working if you'd like someone to check it.

Edit: Last post for today.
Yeah it was my working, thanks.

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