Projecting a vector to another vector
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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.
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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)
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1 Comment
Accepted Answer
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)
4 Comments
More Answers (9)
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)
5 Comments
Jan
on 1 Mar 2011
What exactly does "but it does not work" mean?
Your solution 1:
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.
Your solution 2: wrong
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 Comments
Paulo Silva
on 1 Mar 2011
I failed somehow to find the function dot and done sum(A.*B) instead :) but the results are the same
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.
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).
0 Comments
fatema hasan
on 13 Dec 2020
- Write the complete MATLAB commands to find the unit vector parallel to the projection of #5
0 Comments
fatema hasan
on 13 Dec 2020
- If A= <1,2,3>, B = <4,5,6>, write the complete MATLAB commands to compute the projection of A on B
0 Comments
fatema hasan
on 13 Dec 2020
- Compute the partial derivative of x2y3sin(e2xy) in MATLAB with respect to y
Answer:
Syms x,y,z
f=x^2 + y^3 + sin(x*y);
diff(f,x)
diff(f,y)
0 Comments
fatema hasan
on 13 Dec 2020
- Given two vectors: <1,4,3> and <1,0, -2>
Write the complete MATLAB commands to find the dot product
0 Comments
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]
0 Comments
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