Dot product of two vector

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Syazana 2023-8-27

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https://ww2.mathworks.cn/matlabcentral/answers/2013642-dot-product-of-two-vector

编辑： David Goodmanson 2023-8-28

Hello, I want to find the dot product of this two vector. Can anyone help me in the simple way

A=[c1 -s1 0
    s1 c1 0
    0 0 1]
N= [n1
    n2
    n3]

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Star Strider 2023-8-27

在 MATLAB Online 中打开

Is ‘a1’ supposed to be ‘A(1,:)’ or ‘A(:,1)’?

Experiment with these options —

syms c1 n1 n2 n3 s1 real

A = [c1 -s1 0; s1 c1 0; 0 0 1];

N = [n1; n2; n3];

An = A * N % Original 'A'

An =

AtN = A' * N % Transposed 'A'

AtN =

.

Syazana 2023-8-27

编辑：Syazana 2023-8-27

Ok. Thank you so much. I change the N=[a1,a2,a3] and im using the first answer. Already got the answer. but how to set the coding if a3.n2 the answer will be in scalar which is 0 and if a3.n3 the answer will be 1. In the other words, if the vector multiply by the same vector the answer is 1 if not the answer will be 0

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Answer 1

David Goodmanson 2023-8-28

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https://ww2.mathworks.cn/matlabcentral/answers/2013642-dot-product-of-two-vector#answer_1294677

编辑：David Goodmanson 2023-8-28

在 MATLAB Online 中打开

Hello Syazana

syms c1 s1 n1 n2 n3 a1 a2 a3 real
A = [c1 -s1 0; s1 c1  0; 0  0   1]
    A =
    [c1, -s1, 0]
    [s1,  c1, 0]
    [ 0,   0, 1]
a1 = [1 0 0]';     % all of these are column vectors
a2 = [0 1 0]';
a3 = [0 0 1]';
n1 = [1 0 0]';
n2 = [0 1 0]';
n3 = [0 0 1]';
n1'*A*a1          % n1' is a row vector
  ans = c1
n2'*A*a1          % A(2,1)
  ans = s1
n1'*A*a2          % A(1,2)
  ans = -s1
n3'*A*a3
  ans = 1

As you can see, n1',n2', or n3' select out the row of A, and a1,a2, or a3 select out the column of A. As indicated in two comments above, the typograpy allows you to directly read off the resulting element of A. Doing the matrix multiplication by hand on a couple of examples will convince you how this works.