# Projecting a vector to another vector

911 views (last 30 days)
Victor on 28 Feb 2011
Answered: Brandon O'Neill on 26 Mar 2021
I would like to project a vector to another vector. You can find more information here:
For example I would like to project vector A to vector B. I have used these tricks but it does not work: Any comment is appreciated.
-----------------------
Solution 1)
A=[-10,10,0];
B=[0,0,1];
C=(dot(A,B)/norm(B)^2)*B
---------------------------------
Solution 2)
A=[-10,10,0];
B=[0,0,1];
CosTheta = dot(A,B)/(norm(A)*norm(B));
ThetaInDegrees = acos(CosTheta)*180/pi;
c=norm(A)*cos(ThetaInDegrees)
-----------------------------
Matt Fig on 2 Mar 2011

Jan on 1 Mar 2011
You have to tell DOT, that it must work on the 2nd dimension. Finally BSXFUN is needed to multiply the [88 x 1] and the [88 x 3] arrays. Unfortunalely NORM replies a matrix norm when operating on a matrix. Either use DNorm2: http://www.mathworks.com/matlabcentral/fileexchange/29035-dnorm2 or create the vector norm manually:
A = repmat([10,10,-10] ,[88,1]);
B = repmat([1,1,-1], [88,1]);
lenC = dot(A, B, 2) ./ sum(B .* B, 2); % EDITED, twice
C = bsxfun(@times, lenC, B)
Jan on 4 Mar 2011
Thanks Matt, fixed.

Paulo Silva on 28 Feb 2011
A=[-10,10,0];
B=[0,0,1];
%calculation of the projection of A into B
C=(sum(A.*B)/(norm(B)^2))*B;
%versors of each vector
An=A/norm(A);
Bn=B/norm(B);
Cn=C/norm(C);
%graphic representation
clf
line([0 A(1)],[0 A(2)],[0 A(3)],'LineWidth',10,'Color',[0 0 1])
line([0 B(1)],[0 B(2)],[0 B(3)],'LineWidth',8,'Color',[0 1 0])
line([0 C(1)],[0 C(2)],[0 C(3)],'LineWidth',5,'Color',[1 0 0])
legend('A','B','proj A into B')
xlabel('X')
ylabel('Y')
zlabel('Z')
view(80,10)
Victor on 1 Mar 2011
Dear Paulo and Matt

Jan on 1 Mar 2011
What exactly does "but it does not work" mean?
A = [-10,10,0];
B = [0,0,1];
C = (dot(A,B)/norm(B)^2)*B
This looks ok. If you get C = [0,0,0], the method works. A and B are orthogonal, such that the projection is zero.
CosTheta = dot(A,B)/(norm(A)*norm(B));
ThetaInDegrees = acos(CosTheta)*180/pi;
c=norm(A)*cos(ThetaInDegrees)
Now c is a scalar, but you wanted a vector. Converting Theta in degrees is not correct here: COS works win radians. Use COSD for degerees. Improved:
CosTheta = dot(A,B) / (norm(A)*norm(B));
C = norm(A) * CosTheta * B / norm(B);
And as expected: If you insert CosTheta in the 2nd line, you get your solution 1 again.
##### 2 CommentsShowHide 1 older comment
Jan on 1 Mar 2011
sum(A.*B) and A*B' are faster then DOT. But for [1 x 3] vectors this does not matter.

Victor on 1 Mar 2011
Dear all,
Let me describe the problem. Actually I have two n*3 matrices that I should project one of them to another one.(I use dlmread to read these files) Every raw of these matrices are components of separate vectors. in another word, first columns are "x" values, second columns are "y" values and third columns are "z" values--> That is the reason why by mistake I selected two perpendicular vectors in my example :)
Lets assume we have these matrices:
AA=[10,10,-10];
A=repmat(AA,[88,1]);% lets assume this is my first matrix
BB=[1,1,-1];
B=repmat(BB,[88,1]); % and for example this is my second matrix that I am going to project the A matrix to it
%CC = (dot(AA,BB)/norm(BB).^2)*BB %in this case it will project the AA matrix to BB matrix
C = (dot(A,B)/norm(B).^2)*B % but for this one it gives the error of "Inner matrix dimensions must agree", that is because (dot(A,B)/norm(B).^2) is a 1*3 matrix and B is a 88*3 matrix or maybe because of another reason because when I change B matrix to BB matrix, still I have the same problem!!

Foday Samura on 1 May 2020
Find the length (or norm) of the vector that is the orthogonal projection of the vector a = [ 1 2 4 ] onto b = [6 10 3 ]. Type an answer that is accurate to 3 decimal places. (For example, if your answer is 4+2/3, you should type 4.667).

fatema hasan on 13 Dec 2020
1. Write the complete MATLAB commands to find the unit vector parallel to the projection of #5

fatema hasan on 13 Dec 2020
1. If A= <1,2,3>, B = <4,5,6>, write the complete MATLAB commands to compute the projection of A on B

fatema hasan on 13 Dec 2020
1. Compute the partial derivative of x2y3sin(e2xy) in MATLAB with respect to y
Syms x,y,z
f=x^2 + y^3 + sin(x*y);
diff(f,x)
diff(f,y)

fatema hasan on 13 Dec 2020
1. Given two vectors: <1,4,3> and <1,0, -2>
Write the complete MATLAB commands to find the dot product

Brandon O'Neill on 26 Mar 2021
At a certain time of day the radiant energy from the sun reaches the roof along the direction given by the unit vector
The fraction of the sun’s energy which is falling perpendicularly on the roof is the projection of vector (A) onto the direction perpendicular to the roof – this is the dot product of (A) with the unit vector.
Q1) Use Matlab to calculate the fraction of the sun’s energy which is falling perpendicularly on the roof.
can anyone help with this?
the univ vector is [0.7627;0.5509;0.3390]
the vector A = 1/sqrt(21)[1;2;-4]