Question

Please help with this vectors question



Write a vector equation and a scalar equation of the plane.

Parallel to the plane 3x - 9y + z - 12 = 0 and including the point (-3, 7, 1)

Answer at the back of the textbook:
[x, y, z] = [-3, 7, 1] + s[3, 1, 0] + t[1, 0, -3]
3x - 9y + z + 71 = 0

Please show all work! Thanks :)

Answer 1

Is this correct? Starts from the top.

Answer 2

It looks correct to me.

Answer 3

But is there anything that I can change so its not "copying"?

Answer 4

and isnt there supposed to be 3 terms instead of 2 for the final answer?

Answer 5

like [x,y,z]=[a,b,c]+s[d,e,f]+t[g,h,i] instead of,
[x,y,z]=[a,b,c]+s[d,e,f]

Answer 6

@KingGeorge ?

Answer 7

I did up to the scalar equation which is,
3x - 9y + z + 71 = 0
I just need help with the vector equation now

Answer 8

OK, there are supposed to be 3 terms instead of two. Whoever wrote on that paper gave you the first two terms. Now you just need the 3rd. To do that, find another point in the plane.

Answer 9

Ok, so can it be [-1, 2, 5]?

Answer 10

By the way, what point did they use?

Answer 11

You need to make sure that it works with the equation 3x-9y+z+71=0, so (-1, 2, 5) would not work. To make this work, choose an x value, and a y value, and solve for z.

They used the point (2, 1, -68)

Answer 12

How about, [3, -10, 10] ?

Answer 13

**[3, 10, 10]

Answer 14

Let x=3, y=10. That means you have \[3(3)-9(10)+z+71=-81+71+z=-10+z\]So that point should work.

Answer 15

Now, what's the vector from (-3, 7, 1) to that new point?

Answer 16

[3, 10, 10] - [-3, 7, 1]
[-3-3, 7-10, 1-10]
[-6, -3, -9]
?

Answer 17

Just about. It should be [6, -3, -9]. This is the second vector you need for your equation.

Answer 18

-3-3=-6

Answer 19

It should be \(3-(-3)=6\).

Answer 20

why though? I thought it was right - left?

Answer 21

It's the second point - the first point. We're using the second point as (3, 10, 10) and the first as (-3, 7, 1). You even typed the first part correctly.

Now that I think about it, all the negatives should be reversed. So your vector should be (6, 3, 9)

Answer 22

And what about the previous question, The points were [-1, 0, 0] and [-1, 3, 4] and the point that was given was [-1, -2, -5]

Answer 23

The point was actually [-1, -2, 5], and the vector (for the second one) was [-1,3,4]-[-1,-2,5]=[0,3-(-2),4-5]=[0,5,-1]

Answer 24

Oh yea my fault

Answer 25

Ok, so the answer is,
[x, y, z] = [-3, 7, 1] + ?

Answer 26

The first vector that was written on the paper, which is [5, -6, 69] and the vector we just derived here which is [6, 3, 9].

Answer 27

which is multiplied by s?

Answer 28

It doesn't matter. As long as one is multiplied by s, and the other by t, you should be fine.

Answer 29

I see, THANKS AGAIN! Sorry for bothering you so much :P
Have a good day! :)