# Finding angles in the xy plane with vectors Watch

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#2

(Original post by

Here is the question.

**Mad Man**)Here is the question.

If so, then you just need to realise that the equation of the xy-plane is simply .

Last edited by RDKGames; 3 weeks ago

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(Original post by

I assume you would know how to answer this if you were given the equation of the plane in the form ??

If so, then you just need to realise that the equation of the xy-plane is simply .

**RDKGames**)I assume you would know how to answer this if you were given the equation of the plane in the form ??

If so, then you just need to realise that the equation of the xy-plane is simply .

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#5

(Original post by

No can you explain?

**Mad Man**)No can you explain?

Suppose we have some plane and a line going through it. The angle between these is marked as . One approch to determine it, is to firstly determine what is, which is presicely the angle between the normal to the plane, , and the line . If you can do that, then it's a simple matter of realising that , therefore our angle is given by .

In your question, you can think of as being your vector , and the plane being the xy-plane . Have a go.

No fully worked solutions will be provided to you, it's not the kind of site where others do your work for you. Post your working out if you get stuck.

Last edited by RDKGames; 3 weeks ago

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(Original post by

Okay then, I presume you know how to find an angle between two lines which intersect in 3D, or more specifically, how to find the angle between any two vectors. Look at the diagram below.

Suppose we have some plane and a line going through it. The angle between these is marked as . One approch to determine it, is to firstly determine what is, which is presicely the angle between the normal to the plane, , and the line . If you can do that, then it's a simple matter of realising that , therefore our angle is given by .

In your question, you can think of as being your vector , and the plane being the xy-plane . Have a go.

No fully worked solutions will be provided to you, it's not the kind of site where others do your work for you. Post your working out if you get stuck.

**RDKGames**)Okay then, I presume you know how to find an angle between two lines which intersect in 3D, or more specifically, how to find the angle between any two vectors. Look at the diagram below.

Suppose we have some plane and a line going through it. The angle between these is marked as . One approch to determine it, is to firstly determine what is, which is presicely the angle between the normal to the plane, , and the line . If you can do that, then it's a simple matter of realising that , therefore our angle is given by .

In your question, you can think of as being your vector , and the plane being the xy-plane . Have a go.

No fully worked solutions will be provided to you, it's not the kind of site where others do your work for you. Post your working out if you get stuck.

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#8

(Original post by

I'm so confused, please give me a worked example. I am studying on my own so this isn't for homework.

**Mad Man**)I'm so confused, please give me a worked example. I am studying on my own so this isn't for homework.

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(Original post by

Have you covered how to find angles between two vectors, or is that over your head as well?

**RDKGames**)Have you covered how to find angles between two vectors, or is that over your head as well?

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**RDKGames**)

Have you covered how to find angles between two vectors, or is that over your head as well?

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**RDKGames**)

Have you covered how to find angles between two vectors, or is that over your head as well?

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**RDKGames**)

Okay then, I presume you know how to find an angle between two lines which intersect in 3D, or more specifically, how to find the angle between any two vectors. Look at the diagram below.

Suppose we have some plane and a line going through it. The angle between these is marked as . One approch to determine it, is to firstly determine what is, which is presicely the angle between the normal to the plane, , and the line . If you can do that, then it's a simple matter of realising that , therefore our angle is given by .

In your question, you can think of as being your vector , and the plane being the xy-plane . Have a go.

No fully worked solutions will be provided to you, it's not the kind of site where others do your work for you. Post your working out if you get stuck.

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#15

(Original post by

Can you explain the answer?

**Mad Man**)Can you explain the answer?

Find the angle between the vector and the xy-plane.

Hopefully the diagram below helps you visualise this vector, as well as the xy plane. The red plane is the xy plane, and the pink vector is our vector. I have labelled the three components for you on the diagram as well, the 1 across in the x direction, 2 in the y dir, and 3 up in the z dir.

In the second diagram, I have drawn on a teal length which is contained ENTIRELY in the xy plane. It's a two dimensional vector, hopefully you can see how it is the vector . And because this vector is entirely in the xy plane, then our problem of finding the angle between the pink vecotr and the xy plane, reduces to finding the angle between the pink vector and our teal vector.

What we have going on here are two right-angled triangles to help us do that. One that is lying flat on the xy plane, with sides 1 and 2, and another that is standing upright in the same plane as the pink and teal vector.

Using basic Pythagoras on the flat triangle, you can determine the length of the teal line, and then use basic trig on the standing triangle to determine the angle , because notice that (pink length)*cos(theta) = (teal length). Hence you can work out what cos(theta) is and hence what theta is.

Last edited by RDKGames; 3 weeks ago

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#16

(Original post by

Oh I get it now! But why is z=0?

**Mad Man**)Oh I get it now! But why is z=0?

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(Original post by

On the xy-plane, every single point has z coordinate as zero. So the entire plane is described by the equation .

**RDKGames**)On the xy-plane, every single point has z coordinate as zero. So the entire plane is described by the equation .

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#18

(Original post by

Thanks, how do I increase my visualisation skills?

**Mad Man**)Thanks, how do I increase my visualisation skills?

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(Original post by

Practice more questions with vectors and planes, including sketching them. Really they're not going to come up in A-level maths but if you're interested then have a look at the vectors topics in AS further maths.

**Sinnoh**)Practice more questions with vectors and planes, including sketching them. Really they're not going to come up in A-level maths but if you're interested then have a look at the vectors topics in AS further maths.

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#20

(Original post by

Can you explain the answer the textbook gave (above).

**Mad Man**)Can you explain the answer the textbook gave (above).

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