Angle between a vector and xy, xz, and yz planes

Hi

I have a vector defined by P1. [12,14,78]

How can I caculate the angle this forms with the xy, xz an yz planes pls.

I can do with atan(x/y) etc, but this is problematic when the angle is over 90 or 180.

What would be the best approach pls

[Matt J]

but this is problematic when the angle is over 90 or 180.

It is not possible for a vector to form an angle of more than 90 degrees to a plane

[Mel A]

Thanks very much,

I think I havent worded my question clearly, I have attached an image. It the angle in the x,y plane from the x axis (or y and so on)

When I use ATAN(x/y) etc I get the angle that I can see off the screen. But the direction is the problem.

When I canculate with he method given here in teh comment, the numbers are different to what I get off the screen.

Thanks ever so much

[Bruno Luong]

From your graph it looks to me the angles are between vector P and basis vectors and not the planes

[Mel A]

Yes, you are right. Angle with the base vector on xy( or other) plane. How could I calculate it allowing for more than 90 deg angles Pls. Thanks a lot

Answer 1

[Bruno Luong]

P1=[12,14,78]

P1 = 1×3

12 14 78

xyzc=num2cell(eye(3),1)

xyzc = 1×3 cell array
    {3×1 double}    {3×1 double}    {3×1 double}

[x,y,z]=deal(xyzc{:});
rad2deg(subspace(P1(:),[x y]))

ans = 76.6995

rad2deg(subspace(P1(:),[x z]))

ans = 10.0596

rad2deg(subspace(P1(:),[y z]))

ans = 8.6107

Answer 2

[Matt J]

P1=[12,14,78];

Angles = 90 - acosd(normalize(flip(P1),'n'))

Angles = 1×3

76.6995 10.0596 8.6107