Dot product of two vector

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]

[the cyclist]

"A" is not a vector. It is a matrix. You cannot take the dot product of a matrix and a vector.

Maybe you mean that you just want the matrix product? Or maybe you want the dot product of N with each column of A?

You need to clarify your question.

[Syazana]

Here is the table of cosine which contain vector n1,n2,n3 and a1,a2,a3

Let's say if vector n1 x vector a1, I want the answer to be c1

[Star Strider]

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]

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

Answer 1

[David Goodmanson]

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.

Answer 2

[Star Strider]

My pleasure!

‘... 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 ...’

If you changed ‘N’ to:

N=[a1,a2,a3]

and unless ‘A’ changed to something else as well (and was not posted), the ‘n’ elements no longer exist, so I am now lost.

syms a1 a2 a3 c1 s1 real
A = [c1 -s1 0; s1 c1  0; 0  0   1];
N = [a1; a2; a3];

An = A * N                                      % Original 'A'

An = 

In any event, to change symbolic variables to something else, use the subs function.

.