What should be the angle between two vectors A and B for their resultant R to be a maximum and B minimum?

Edited: MathWorks Support Team on 27 May 2020

There is no in-built MATLAB function to find the angle between two vectors. As a workaround, you can try the following:

CosTheta = max(min(dot(u,v)/(norm(u)*norm(v)),1),-1);

ThetaInDegrees = real(acosd(CosTheta));

So why doesn't matlab give us a function for that instead of having us look endlessly on forums?

Edited: James Tursa on 5 Jan 2019

This topic has been discussed many times on the Newsgroup forum ... if I looked hard enough I'm sure I could find several Roger Stafford posts from many years ago on this. E.g., here is one of them:

The basic acos formula is known to be inaccurate for small angles. A more robust method is to use both the sin and cos of the angle via the cross and dot functions. E.g.,

atan2(norm(cross(u,v)),dot(u,v));

An extreme case to clearly show the difference:

>> v = 5*[cos(a) sin(a) 0]

>> acos(dot(u,v)/(norm(u)*norm(v)))

>> atan2(norm(cross(u,v)),dot(u,v))

Edited: Gabor Bekes on 15 Sep 2016

This does the same thing, also capable of determining the angle of higher (than one) dimensional subspaces.

subspace(vector1,vector2)

Just a note on how to vectorize the whole thing: (semicolons purposely omitted to see the intermediate results)

ThetaInDegrees = atan2d(NC,D)

vThetaInDegrees = mean(atan2d(vNC,vD))

or in short (the hard to read variant)

VThetaInDegrees =atan2d( vecnorm(cross(Vu,Vv,2),2,2) , dot(Vu,Vv,2) )

Coordinates of two vectors xb,yb and xa,ya .

angle(vector.b,vector.a)=pi/2*((1+sgn(xa))*(1-sgn(ya^2))-(1+sgn(xb))*(1-sgn(yb^2)))

+pi/4*((2+sgn(xa))*sgn(ya)-(2+sgn(xb))*sgn(yb))

+sgn(xa*ya)*atan((abs(xa)-abs(ya))/(abs(xa)+abs(ya)))

-sgn(xb*yb)*atan((abs(xb)-abs(yb))/(abs(xb)+abs(yb)))

Edited: Mahaveer Singh on 4 May 2021

function angle_in_degrees = vector2angle(u,v)

a= sqrt(u(1)^2+u(2)^2+u(3)^2);

b=sqrt(v(1)^2+v(2)^2+v(3)^2);

angle_in_degrees=acos(c/(a*b))*180/pi

Currently, there is no built-in MATLAB function to calculate the angle between two vectors. However, you can use dot product property of two vectors to find the angle:

cosOfAngle = max(min(dot(u,v)/(norm(u)*norm(v)),1),-1);

angleInDegrees = real(acosd(cosOfAngle));